The Experts below are selected from a list of 76434 Experts worldwide ranked by ideXlab platform
Peter C B Phillips - One of the best experts on this subject based on the ideXlab platform.
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random coefficient continuous systems testing for extreme Sample Path behaviour
2017Co-Authors: Yubo Tao, Peter C B PhillipsAbstract:This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme Sample Path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S\&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices.
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random coefficient continuous systems testing for extreme Sample Path behaviour
Social Science Research Network, 2017Co-Authors: Yubo Tao, Peter C B PhillipsAbstract:This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, the asymptotic theory is developed, and test statistics to identify the different forms of extreme Sample Path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S&P500 index data over 1928-2018 reveals strong evidence against parameter constancy over the whole Sample period leading to a long duration of what the model characterizes as extreme behaviour in real stock prices.
Yimin Xiao - One of the best experts on this subject based on the ideXlab platform.
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linear fractional stable sheets wavelet expansion and Sample Path properties
Stochastic Processes and their Applications, 2009Co-Authors: Antoine Ayache, Francois Roueff, Yimin XiaoAbstract:Abstract In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in [A. Ayache, F. Roueff, Y. Xiao, Local and asymptotic properties of linear fractional stable sheets, C.R. Acad. Sci. Paris Ser. I. 344 (6) (2007) 389–394]. By using this representation, in the case where the Sample Paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these Paths is obtained as well as an upper bound for their behavior at infinity and around the coordinate axes. The Hausdorff dimensions of the range and graph of these stable random fields are then derived.
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Sample Path properties of anisotropic gaussian random fields
2009Co-Authors: Yimin XiaoAbstract:Anisotropic Gaussian random flelds arise in probability theory and in various applications. Typical examples are fractional Brownian sheets, operator-scaling Gaussian flelds with stationary increments, and the solution to the stochastic heat equation. This paper is concerned with Sample Path properties of anisotropic Gaussian random flelds in general. Let X = fX(t); t 2 R N g be a Gaussian random fleld with values in R d and with parameters H1;:::;HN. Our goal is to characterize the anisotropic nature of X in terms of its parameters explicitly. Under some general conditions, we establish results on the modulus of continuity, small ball probabilities, fractal dimensions, hitting probabilities and local times of anisotropic Gaussian random flelds. An important tool for our study is the various forms of strong local nondeterminism.
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linear fractional stable sheets wavelet expansion and Sample Path properties
arXiv: Statistics Theory, 2008Co-Authors: Antoine Ayache, Francois Roueff, Yimin XiaoAbstract:In this paper we give a detailed description of the random wavelet series representation of real-valued linear fractional stable sheet introduced in Ayache, Roueff and Xiao (2007). By using this representation, in the case where the Sample Paths are continuous, an anisotropic uniform and quasi-optimal modulus of continuity of these Paths is obtained as well as an upper bound for their behavior at infinity and around the coordinate axes. The Hausdorff dimensions of the range and graph of these stable random fields are then derived.
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Sample Path properties of bifractional brownian motion
Bernoulli, 2007Co-Authors: Ciprian A Tudor, Yimin XiaoAbstract:Let B H;K = ' B H;K (t); t 2R+ “ be a bifractional Brownian motion in R d . We prove that B H;K is strongly locally nondeterministic. Applying this property and a stochastic integral representation of B H;K , we establish Chung’s law of the iterated logarithm for
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Sample Path properties of bifractional brownian motion
arXiv: Probability, 2006Co-Authors: Ciprian A Tudor, Yimin XiaoAbstract:Let $B^{H, K}= \big\{B^{H, K}(t), t \in \R_+ \big\}$ be a bifractional Brownian motion in $\R^d$. We prove that $B^{H, K}$ is strongly locally nondeterministic. Applying this property and a stochastic integral representation of $B^{H, K}$, we establish Chung's law of the iterated logarithm for $B^{H, K}$, as well as sharp H\"older conditions and tail probability estimates for the local times of $B^{H, K}$. We also consider the existence and the regularity of the local times of multiparameter bifractional Brownian motion $B^{\bar{H}, \bar{K}}= \big\{B^{\bar{H}, \bar{K}}(t), t \in \R^N_+ \big\}$ in $\R^d$ using Wiener-It\^o chaos expansion.
Giovanni Luca Torrisi - One of the best experts on this subject based on the ideXlab platform.
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Sample Path large deviations of poisson shot noise with heavy tailed semiexponential distributions
Journal of Applied Probability, 2011Co-Authors: Ken R Duffy, Giovanni Luca TorrisiAbstract:The problem of finding network codes for general connections is inherently difficult. Resource minimization for general connections with network coding is further complicated. The existing solutions mainly rely on very restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a Constraint Satisfaction Problem (CSP) which we show can be simplified to have a moderate number of constraints. While CSPs are NP-complete in general, we present a probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation.
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Sample Path large deviations principles for poisson shot noise processes and applications
Electronic Journal of Probability, 2005Co-Authors: Ayalvadi Ganesh, Claudio Macci, Giovanni Luca TorrisiAbstract:This paper concerns Sample Path large deviations for Poisson shot noise processes, and applications in queueing theory. We first show that, under an exponential tail condition, Poisson shot noise processes satisfy a Sample Path large deviations principle with respect to the topology of pointwise convergence. Under a stronger superexponential tail condition, we extend this result to the topology of uniform convergence. We also give applications of this result to determining the most likely Path to overflow in a single server queue, and to finding tail asymptotics for the queue lengths at priority queues.
Stephen M Robinson - One of the best experts on this subject based on the ideXlab platform.
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Sample Path solution of stochastic variational inequalities
Mathematical Programming, 1999Co-Authors: G Gurkan, Yonca A Ozge, Stephen M RobinsonAbstract:Sample-Path optimization is a simulation-based method for solving optimization problems that arise in the study of complex stochastic systems. In this paper we broaden its applicability to include the solution of stochastic variational inequalities. This formulation can model equilibrium phenomena in physics, economics, and operations research. We describe the method, provide general conditions for convergence, and present numerical results of an application of the method to a stochastic economic equilibrium model of the European natural gas market. We also point out some current limitations of the method and indicate areas in which research might help to remove those limitations.
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Sample Path solution of stochastic variational inequalities with applications to option pricing
Winter Simulation Conference, 1996Co-Authors: G Gurkan, Yonca A Ozge, Stephen M RobinsonAbstract:This paper shows how to apply a variant of Sample Path optimization to solve stochastic variational in equalities, including as a special case finding a zero of a gradient. We give a new set of sufficient conditions for almost-sure convergence of the method, and exhibit bounds on the error of the resulting approximate solution. We also illustrate the application of this method by using it to price an American call option on a dividend-paying stock.
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Sample-Path optimization of convex stochastic performance functions
Mathematical Programming, 1996Co-Authors: Erica L. Plambeck, Stephen M Robinson, Rajan SuriAbstract:In this paper we propose a method for optimizing convex performance functions in stochastic systems. These functions can include expected performance in static systems and steady-state performance in discrete-event dynamic systems; they may be nonsmooth. The method is closely related to retrospective simulation optimization; it appears to overcome some limitations of stochastic approximation, which is often applied to such problems. We explain the method and give computational results for two classes of problems: tandem production lines with up to 50 machines, and stochastic PERT (Program Evaluation and Review Technique) problems with up to 70 nodes and 110 arcs.
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analysis of Sample Path optimization
Mathematics of Operations Research, 1996Co-Authors: Stephen M RobinsonAbstract:Sample-Path optimization is a method for optimizing limit functions occurring in stochastic modeling problems, such as steady-state functions in discrete-event dynamic systems. It is closely related to retrospective optimization techniques and to M-estimation. The method has been computationally tested elsewhere on problems arising in production and in project planning, with apparent success. In this paper we provide a mathematical justification for Sample-Path optimization by showing that under certain assumptions---which hold for the problems just mentioned---the method will almost surely find a point that is, in a specified sense, sufficiently close to the set of optimizers of the limit function.
Yubo Tao - One of the best experts on this subject based on the ideXlab platform.
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random coefficient continuous systems testing for extreme Sample Path behaviour
2017Co-Authors: Yubo Tao, Peter C B PhillipsAbstract:This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, asymptotic theory is developed, and test statistics to identify the different forms of extreme Sample Path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S\&P 500 index data over 1964-2015 reveals strong evidence against parameter constancy after early 1980, which strengthens after July 1997, leading to a long duration of what the model characterizes as extreme behaviour in real stock prices.
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random coefficient continuous systems testing for extreme Sample Path behaviour
Social Science Research Network, 2017Co-Authors: Yubo Tao, Peter C B PhillipsAbstract:This paper studies a continuous time dynamic system with a random persistence parameter. The exact discrete time representation is obtained and related to several discrete time random coefficient models currently in the literature. The model distinguishes various forms of unstable and explosive behaviour according to specific regions of the parameter space that open up the potential for testing these forms of extreme behaviour. A two-stage approach that employs realized volatility is proposed for the continuous system estimation, the asymptotic theory is developed, and test statistics to identify the different forms of extreme Sample Path behaviour are proposed. Simulations show that the proposed estimators work well in empirically realistic settings and that the tests have good size and power properties in discriminating characteristics in the data that differ from typical unit root behaviour. The theory is extended to cover models where the random persistence parameter is endogenously determined. An empirical application based on daily real S&P500 index data over 1928-2018 reveals strong evidence against parameter constancy over the whole Sample period leading to a long duration of what the model characterizes as extreme behaviour in real stock prices.
