The Experts below are selected from a list of 26061 Experts worldwide ranked by ideXlab platform

Jinghai Shao - One of the best experts on this subject based on the ideXlab platform.

  • criteria for transience and recurrence of regime switching diffusion processes
    Electronic Journal of Probability, 2015
    Co-Authors: Jinghai Shao
    Abstract:

    We provide some criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a Finite space or in an inFinite countable space are all studied in this work. Especially, we put forward a Finite Partition method to deal with switching processes in an inFinite countable space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide a necessary and sufficient condition for a kind of nonlinear regime-switching diffusion processes.

  • Criteria for transience and recurrence of regime-switching diffusion processes *
    Electronic Journal of Probability, 2015
    Co-Authors: Jinghai Shao
    Abstract:

    We provide some criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a Finite space or in an inFinite countable space are all studied in this work. Especially, we put forward a Finite Partition method to deal with switching processes in an inFinite countable space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide a necessary and sufficient condition for a kind of nonlinear regime-switching diffusion processes.

  • Approximation of Invariant Measures for Regime-Switching Diffusions
    arXiv: Probability, 2014
    Co-Authors: Jinghai Shao, Chenggui Yuan
    Abstract:

    In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with a range of regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for regime-switching diffusion processes with Finite state spaces by the Perron-Frobenius theorem if the "averaging condition" holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for regime-switching diffusion processes with countable state spaces by means of a Finite Partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.

  • criteria for transience and recurrence of regime switching diffusion processes
    arXiv: Probability, 2014
    Co-Authors: Jinghai Shao
    Abstract:

    We provide some on-off type criteria for recurrence and transience of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a Finite space and a countable space are both studied. We put forward a Finite Partition method to deal with switching process in a countable space. As an application, we improve the known criteria for recurrence of linear regime-switching diffusion processes, and provide an on-off type criterion for a kind of nonlinear regime-switching diffusion processes.

  • Ergodicity of regime-switching diffusions in Wasserstein distances
    arXiv: Probability, 2014
    Co-Authors: Jinghai Shao
    Abstract:

    Based on the theory of M-matrix and Perron-Frobenius theorem, we provide some criteria to justify the convergence of the regime-switching diffusion processes in Wasserstein distances. The cost function we used to define the Wasserstein distance is not necessarily bounded. The continuous time Markov chains with Finite and countable state space are all studied. To deal with the countable state space, we put forward a Finite Partition method. The boundedness for state-dependent regime-switching diffusions in an inFinite state space is also studied.

Guilin Yang - One of the best experts on this subject based on the ideXlab platform.

  • Workspace evaluation of manipulators through Finite-Partition of SE(3)
    Robotics and Computer-Integrated Manufacturing, 2011
    Co-Authors: Yan Jin, I-ming Chen, Guilin Yang
    Abstract:

    Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-D space, it is difficult to quantify and qualify it. Most literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a Finite-Partition approach of the Special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of Special Orthogonal group SO(3) and R^3. It is known that the SO(3) is homeomorphic to a solid ball D^3 with antipodal points identified while the geometry of R^3 can be regarded as a cuboid. The complete 6-D workspace SE(3) is at the first time parametrically and proportionally Partitioned into a number of elements with uniform convergence based on its geometry. As a result, a basis volume element of SE(3) is formed by the product of a basis volume element of R^3 and a basis volume element of SO(3), which is the product of a basis volume element of D^3 and its associated integration measure. By this way, the integration of the complete 6-D workspace volume becomes the simple summation of the basis volume elements of SE(3). Two new global performance indices, i.e., workspace volume ratio (W"r) and global condition index (GCI), are defined over the complete 6-D workspace. A newly proposed 3RP PS parallel manipulator is optimized based on this Finite-Partition approach. As a result, the optimal dimensions for maximal workspace are obtained, and the optimal performance points in the workspace are identified.

  • Numerical Orientation Workspace Analysis with Different Parameterization Methods
    2006 IEEE Conference on Robotics Automation and Mechatronics, 2006
    Co-Authors: Guilin Yang, Shabbir Kurbanhusen Mustafa, I-ming Chen
    Abstract:

    For numerical orientation workspace analysis, a Finite Partition of the orientation workspace in its parametric domain is necessary. Among various parameterization methods for rigid-body rotations, it has been realized that the Euler angles, the tilting-and-torsion (T&T) angles, and the exponential coordinates are appropriate for Finite Partition. With these three parameterization methods, the rigid body rotation group, i.e., the special orthogonal group (SO(3)), can be mapped to a rectangular parallel-piped (for Euler angles), a solid cylinder (for T&T angles), and a solid sphere (for exponential coordinates). To simplify the computation, isotropic/equi-volumetric Partition schemes are proposed for the three geometric entities so that each of them can be geometrically divided into Finite elements with equal volumes. As a result of parameterizations, the volume of orientation workspace, i.e., the volume of SO(3), can be numerically computed as a weighted volume sum of its constituent equi-volumetric elements in which the weightages are the element associated integration measures. Using such Partition schemes, various global performance measures can be readily implemented so as to evaluate the quality of the orientation workspace. A comparison study for the three parameterization methods has shown that the exponential coordinates method is more effective for numerical orientation workspace analysis because it has no formulation singularity and exhibits higher computation accuracy

  • IROS - Finite-Partition of SE(3) and its Applications on Workspace Optimization of Parallel Manipulators
    2006 IEEE RSJ International Conference on Intelligent Robots and Systems, 2006
    Co-Authors: Yan Jin, I-ming Chen, Guilin Yang
    Abstract:

    Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-dimensional space, it is difficult to quantify and qualify it. Most of the literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a Finite-Partition approach of the special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of special orthogonal group SO(3) and Ropf3. It is known that the SO(3) is homeomorphic to a solid ball D3 with antipodal points identified while the geometry of Ropf3 can be regarded as a cuboid. Furthermore, the solid ball and the cuboid can be parametrically and proportionally Partitioned into a number of elements. Therefore, a basis volume element of SE(3) is the product of a basis volume element of Ropf3 and a basis volume element of SO(3), which is the product of a basis volume element of D3 and its associated integration measure. By this way, the integration of the complete 6-D workspace volume become the simple summation of the basis volume elements of SE(3). Two global performance indices, i.e., workspace volume ratio (Wr) and global condition index (GCI)., are defined over the complete 6-D workspace. An optimization algorithm is developed for a 3RPlowbarPS parallel manipulator to illustrate the effectiveness of the Finite-Partition approach. As a result, the workspace optimization method is valid although it is computationally intensive

  • Equivolumetric Partition of solid spheres with applications to orientation workspace analysis of robot manipulators
    IEEE Transactions on Robotics, 2006
    Co-Authors: Guilin Yang, I-ming Chen
    Abstract:

    Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations. For numerical analysis, a Finite Partition of the orientation workspace in its parametric domain is necessary. It has been realized that the exponential coordinates parameterization is more appropriate for Finite Partition. With such a parameterization, the rigid body rotation group, i.e., SO(3), can be mapped to a solid sphere D3 of radius pi with antipodal points identified. A novel Partition scheme is proposed to geometrically divide the parametric domain, i.e., the solid sphere D3 of radius pi, into Finite elements with equal volume. Subsequently, the volume of SO(3) can be numerically computed as a weighted volume sum of the equivolumetric elements, in which the weightages are the element-associated integration measures. In this way, we can simplify the Partition scheme and also reduce the computation efforts, as the elements in the same Partition layer (along the radial direction) have the same integration measure. The effectiveness of the Partition scheme is demonstrated through analysis of the orientation workspace of a three-degree-of-freedom spherical parallel manipulator. Numerical convergence on various orientation workspace measures, such as the workspace volume and the global condition index, are obtained based on this Partition scheme

I-ming Chen - One of the best experts on this subject based on the ideXlab platform.

  • Workspace evaluation of manipulators through Finite-Partition of SE(3)
    Robotics and Computer-Integrated Manufacturing, 2011
    Co-Authors: Yan Jin, I-ming Chen, Guilin Yang
    Abstract:

    Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-D space, it is difficult to quantify and qualify it. Most literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a Finite-Partition approach of the Special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of Special Orthogonal group SO(3) and R^3. It is known that the SO(3) is homeomorphic to a solid ball D^3 with antipodal points identified while the geometry of R^3 can be regarded as a cuboid. The complete 6-D workspace SE(3) is at the first time parametrically and proportionally Partitioned into a number of elements with uniform convergence based on its geometry. As a result, a basis volume element of SE(3) is formed by the product of a basis volume element of R^3 and a basis volume element of SO(3), which is the product of a basis volume element of D^3 and its associated integration measure. By this way, the integration of the complete 6-D workspace volume becomes the simple summation of the basis volume elements of SE(3). Two new global performance indices, i.e., workspace volume ratio (W"r) and global condition index (GCI), are defined over the complete 6-D workspace. A newly proposed 3RP PS parallel manipulator is optimized based on this Finite-Partition approach. As a result, the optimal dimensions for maximal workspace are obtained, and the optimal performance points in the workspace are identified.

  • Numerical Orientation Workspace Analysis with Different Parameterization Methods
    2006 IEEE Conference on Robotics Automation and Mechatronics, 2006
    Co-Authors: Guilin Yang, Shabbir Kurbanhusen Mustafa, I-ming Chen
    Abstract:

    For numerical orientation workspace analysis, a Finite Partition of the orientation workspace in its parametric domain is necessary. Among various parameterization methods for rigid-body rotations, it has been realized that the Euler angles, the tilting-and-torsion (T&T) angles, and the exponential coordinates are appropriate for Finite Partition. With these three parameterization methods, the rigid body rotation group, i.e., the special orthogonal group (SO(3)), can be mapped to a rectangular parallel-piped (for Euler angles), a solid cylinder (for T&T angles), and a solid sphere (for exponential coordinates). To simplify the computation, isotropic/equi-volumetric Partition schemes are proposed for the three geometric entities so that each of them can be geometrically divided into Finite elements with equal volumes. As a result of parameterizations, the volume of orientation workspace, i.e., the volume of SO(3), can be numerically computed as a weighted volume sum of its constituent equi-volumetric elements in which the weightages are the element associated integration measures. Using such Partition schemes, various global performance measures can be readily implemented so as to evaluate the quality of the orientation workspace. A comparison study for the three parameterization methods has shown that the exponential coordinates method is more effective for numerical orientation workspace analysis because it has no formulation singularity and exhibits higher computation accuracy

  • IROS - Finite-Partition of SE(3) and its Applications on Workspace Optimization of Parallel Manipulators
    2006 IEEE RSJ International Conference on Intelligent Robots and Systems, 2006
    Co-Authors: Yan Jin, I-ming Chen, Guilin Yang
    Abstract:

    Workspace analysis and optimization are important in a manipulator design. As the complete workspace of a 6-DOF manipulator is embedded into a 6-dimensional space, it is difficult to quantify and qualify it. Most of the literatures only considered the 3-D sub workspaces of the complete 6-D workspace. In this paper, a Finite-Partition approach of the special Euclidean group SE(3) is proposed based on the topology properties of SE(3), which is the product of special orthogonal group SO(3) and Ropf3. It is known that the SO(3) is homeomorphic to a solid ball D3 with antipodal points identified while the geometry of Ropf3 can be regarded as a cuboid. Furthermore, the solid ball and the cuboid can be parametrically and proportionally Partitioned into a number of elements. Therefore, a basis volume element of SE(3) is the product of a basis volume element of Ropf3 and a basis volume element of SO(3), which is the product of a basis volume element of D3 and its associated integration measure. By this way, the integration of the complete 6-D workspace volume become the simple summation of the basis volume elements of SE(3). Two global performance indices, i.e., workspace volume ratio (Wr) and global condition index (GCI)., are defined over the complete 6-D workspace. An optimization algorithm is developed for a 3RPlowbarPS parallel manipulator to illustrate the effectiveness of the Finite-Partition approach. As a result, the workspace optimization method is valid although it is computationally intensive

  • Equivolumetric Partition of solid spheres with applications to orientation workspace analysis of robot manipulators
    IEEE Transactions on Robotics, 2006
    Co-Authors: Guilin Yang, I-ming Chen
    Abstract:

    Orientation workspace analysis is a critical issue in the design of robot manipulators, especially the spherical manipulators. However, there is a lack of effective methods for such analysis, because the orientation workspace of a robot manipulator is normally a subset of SO(3) (the special orthogonal group) with a complex boundary. Numerical approaches appear more practical in actual implementations. For numerical analysis, a Finite Partition of the orientation workspace in its parametric domain is necessary. It has been realized that the exponential coordinates parameterization is more appropriate for Finite Partition. With such a parameterization, the rigid body rotation group, i.e., SO(3), can be mapped to a solid sphere D3 of radius pi with antipodal points identified. A novel Partition scheme is proposed to geometrically divide the parametric domain, i.e., the solid sphere D3 of radius pi, into Finite elements with equal volume. Subsequently, the volume of SO(3) can be numerically computed as a weighted volume sum of the equivolumetric elements, in which the weightages are the element-associated integration measures. In this way, we can simplify the Partition scheme and also reduce the computation efforts, as the elements in the same Partition layer (along the radial direction) have the same integration measure. The effectiveness of the Partition scheme is demonstrated through analysis of the orientation workspace of a three-degree-of-freedom spherical parallel manipulator. Numerical convergence on various orientation workspace measures, such as the workspace volume and the global condition index, are obtained based on this Partition scheme

Mickael Albertus - One of the best experts on this subject based on the ideXlab platform.

  • Raking-ratio empirical process with auxiliary information learning
    ESAIM: Probability and Statistics, 2020
    Co-Authors: Mickael Albertus
    Abstract:

    The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a Finite Partition. The asymptotic behavior of the raking-ratio empirical process indexed by a class of functions is studied when the auxiliary information is given by estimates. These estimates are supposed to result from the learning of the probability of sets of Partitions from another sample larger than the sample of the statistician, as in the case of two-stage sampling surveys. Under some metric entropy hypothesis and conditions on the size of the information source sample, the strong approximation of this process and in particular the weak convergence are established. Under these conditions, the asymptotic behavior of the new process is the same as the classical raking-ratio empirical process. Some possible statistical applications of these results are also given, like the strengthening of the Z-test and the chi-square goodness of fit test.

  • Raking-ratio empirical process with auxiliary information learning
    2019
    Co-Authors: Mickael Albertus
    Abstract:

    The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets in a Finite Partition. We study the asymptotic behavior of the raking-ratio empirical process indexed by a class of functions when the auxiliary information is given by the learning of the probability of sets in Partitions from another sample larger than the sample of the statistician. Under some metric entropy hypothesis and conditions on the size of the independent samples, we establish the strong approximation of this process with estimated auxiliary information and show in particular that weak convergence is the same as the classical raking-ratio empirical process. We also give possible statistical applications of these results like strengthening the Z-test and the chi-square goodness of fit test.

  • Auxiliary information : the raking-ratio empirical process
    Electronic journal of statistics, 2019
    Co-Authors: Mickael Albertus, Philippe Berthet
    Abstract:

    We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a Finite Partition which changes each step. We establish asymptotic properties of the raking-ratio empirical process indexed by functions as $n\rightarrow +\infty$, for $N$ fixed. We study nonasymptotic properties by using a Gaussian approximation which yields uniform Berry-Esseen type bounds depending on $n, N$ and provides estimates of the uniform quadratic risk reduction. A closed-form expression of the limiting covariance matrices is derived as $N\rightarrow +\infty$. In the two-way contingency table case the limiting process has a simple explicit formula.

Philippe Berthet - One of the best experts on this subject based on the ideXlab platform.

  • Auxiliary information : the raking-ratio empirical process
    Electronic journal of statistics, 2019
    Co-Authors: Mickael Albertus, Philippe Berthet
    Abstract:

    We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a Finite Partition which changes each step. We establish asymptotic properties of the raking-ratio empirical process indexed by functions as $n\rightarrow +\infty$, for $N$ fixed. We study nonasymptotic properties by using a Gaussian approximation which yields uniform Berry-Esseen type bounds depending on $n, N$ and provides estimates of the uniform quadratic risk reduction. A closed-form expression of the limiting covariance matrices is derived as $N\rightarrow +\infty$. In the two-way contingency table case the limiting process has a simple explicit formula.