The Experts below are selected from a list of 150 Experts worldwide ranked by ideXlab platform

Arunabha Bagchi - One of the best experts on this subject based on the ideXlab platform.

  • A representation result for nonlinear filter maps in a white noise framework
    IEEE Transactions on Automatic Control, 1999
    Co-Authors: Ravi R. Mazumdar, Arunabha Bagchi
    Abstract:

    The authors consider the nonlinear filtering model with additive white noise taken to be the identity map on L 2 [0,T] with standard Gauss measure thereon. Using a representation result for maps which are continuous in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators on the Hilbert space, the authors show that the filter map can be written as the composition of a continuous nonlinear map (which does not depend on the observation) with a linear Hilbert-Schmidt Operator acting on the observation. In particular, this result gives a direct proof of existence of approximation of nonlinear filters in terms of Volterra polynomials.

  • A representation result for nonlinear filter maps in a white noise framework
    IEEE Transactions on Automatic Control, 1999
    Co-Authors: Ravi R. Mazumdar, Arunabha Bagchi
    Abstract:

    The authors consider the nonlinear filtering model with additive white noise to be the identity map on L/sub 2/[0,T] with standard Gauss measure thereon. Using a representation result for maps which are continuous in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators on the Hilbert space, the authors show that the filter map can be written as the composition of a continuous nonlinear map (which does not depend on the observation) with a linear Hilbert-Schmidt Operator acting on the observation. In particular, this result gives a direct proof of existence of approximation of nonlinear filters in terms of Volterra polynomials.

  • On input/output maps for nonlinear systems via continuity in a locally convex topology
    Systems and Control Letters, 1995
    Co-Authors: Ravi R. Mazumdar, Raghavan Kannurpatti, Arunabha Bagchi
    Abstract:

    In this paper we show that the output of a nonlinear system with inputs in (L2[0, T]; Rm) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt Operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results. © 1995.

Ravi R. Mazumdar - One of the best experts on this subject based on the ideXlab platform.

  • A representation result for nonlinear filter maps in a white noise framework
    IEEE Transactions on Automatic Control, 1999
    Co-Authors: Ravi R. Mazumdar, Arunabha Bagchi
    Abstract:

    The authors consider the nonlinear filtering model with additive white noise taken to be the identity map on L 2 [0,T] with standard Gauss measure thereon. Using a representation result for maps which are continuous in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators on the Hilbert space, the authors show that the filter map can be written as the composition of a continuous nonlinear map (which does not depend on the observation) with a linear Hilbert-Schmidt Operator acting on the observation. In particular, this result gives a direct proof of existence of approximation of nonlinear filters in terms of Volterra polynomials.

  • A representation result for nonlinear filter maps in a white noise framework
    IEEE Transactions on Automatic Control, 1999
    Co-Authors: Ravi R. Mazumdar, Arunabha Bagchi
    Abstract:

    The authors consider the nonlinear filtering model with additive white noise to be the identity map on L/sub 2/[0,T] with standard Gauss measure thereon. Using a representation result for maps which are continuous in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators on the Hilbert space, the authors show that the filter map can be written as the composition of a continuous nonlinear map (which does not depend on the observation) with a linear Hilbert-Schmidt Operator acting on the observation. In particular, this result gives a direct proof of existence of approximation of nonlinear filters in terms of Volterra polynomials.

  • On input/output maps for nonlinear systems via continuity in a locally convex topology
    Systems and Control Letters, 1995
    Co-Authors: Ravi R. Mazumdar, Raghavan Kannurpatti, Arunabha Bagchi
    Abstract:

    In this paper we show that the output of a nonlinear system with inputs in (L2[0, T]; Rm) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt Operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results. © 1995.

Markus Riedle - One of the best experts on this subject based on the ideXlab platform.

  • Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces: An L2 approach
    Infinite Dimensional Analysis Quantum Probability and Related Topics, 2014
    Co-Authors: Markus Riedle
    Abstract:

    In this work stochastic integration with respect to cylindrical Levy processes with weak second moments is introduced. It is well known that a deterministic Hilbert–Schmidt Operator radonifies a cylindrical random variable, i.e. it maps a cylindrical random variable to a classical Hilbert space valued random variable. Our approach is based on a generalisation of this result to the radonification of the cylindrical increments of a cylindrical Levy process by random Hilbert–Schmidt Operators. This generalisation enables us to introduce a Hilbert space valued random variable as the stochastic integral of a predictable stochastic process with respect to a cylindrical Levy process. We finish this work by deriving an Ito isometry and by considering shortly stochastic partial differential equations driven by cylindrical Levy processes.

  • Stochastic integration with respect to cylindrical Levy processes in Hilbert spaces
    Infinite Dimensional Analysis Quantum Probability and Related Topics, 2014
    Co-Authors: Markus Riedle
    Abstract:

    In this work stochastic integration with respect to cylindrical Lévy processes with weak second moments is introduced. It is well known that a deterministic Hilbert–Schmidt Operator radonifies a cylindrical random variable, i.e. it maps a cylindrical random variable to a classical Hilbert space valued random variable. Our approach is based on a generalisation of this result to the radonification of the cylindrical increments of a cylindrical Lévy process by random Hilbert–Schmidt Operators. This generalisation enables us to introduce a Hilbert space valued random variable as the stochastic integral of a predictable stochastic process with respect to a cylindrical Lévy process. We finish this work by deriving an Itô isometry and by considering shortly stochastic partial differential equations driven by cylindrical Lévy processes.

  • Stochastic integration with respect to cylindrical Levy processes in Hilbert spaces: an L^2 approach
    arXiv: Probability, 2012
    Co-Authors: Markus Riedle
    Abstract:

    In this work stochastic integration with respect to cylindrical Levy processes with weak second moments is introduced. It is well known that a deterministic Hilbert-Schmidt Operator radonifies a cylindrical random variable, i.e. it maps a cylindrical random variable to a classical Hilbert space valued random variable. Our approach is based on a generalisation of this result to the radonification of the cylindrical increments of a cylindrical Levy process by random Hilbert-Schmidt Operators. This generalisation enables us to introduce a Hilbert space valued random variable as the stochastic integral of a predictable stochastic process with respect to a cylindrical Levy process. We finish this work by deriving an Ito isometry and by considering shortly stochastic partial differential equations driven by cylindrical Levy processes.

Leiba Rodman - One of the best experts on this subject based on the ideXlab platform.

  • Two-sided Tangential Interpolation for Hilbert-Schmidt Operator Functions on Polydisks
    Recent Advances in Operator Theory, 2020
    Co-Authors: Daniel Alpay, Vladimir Bolotnikov, Leiba Rodman
    Abstract:

    Bitangential interpolation problems are formulated for the class of Hilbert-Schmidt Operator-valued functions, which are analytic on a polydisk and have square summable power series. A procedure is described for reduction of the problems in d-disk to the analogous problems in (d - 1)-disk. Using this procedure, for the case of the bidisk, the minimal norm solutions are explicitly described in terms of the interpolation data, and formulas for the general solution are obtained.

  • One-Sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bidisk
    Operator Theory Systems Theory and Scattering Theory: Multidimensional Generalizations, 2020
    Co-Authors: M.c.b. Reurings, Leiba Rodman
    Abstract:

    One-sided tangential interpolation problems for functions with symmetries having values in the set of Hilbert-Schmidt Operators and defined on the bidisk are studied. General solutions are described as well as solutions with the minimal scalar and Operator-valued norms. Two types of symmetries are considered: (a) componentwise symmetries that operate separately on each component of a general point in the bidisk; (b) interchange symmetry that interchanges the two components of a general point in the bidisk. Applications are made to multipoint tangential interpolation problems of special form.

Raghavan Kannurpatti - One of the best experts on this subject based on the ideXlab platform.

  • On input/output maps for nonlinear systems via continuity in a locally convex topology
    Systems and Control Letters, 1995
    Co-Authors: Ravi R. Mazumdar, Raghavan Kannurpatti, Arunabha Bagchi
    Abstract:

    In this paper we show that the output of a nonlinear system with inputs in (L2[0, T]; Rm) whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt Operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt Operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results. © 1995.