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Convergence in probability for perturbed stochastic integral equations
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  • Published: April 1989

Convergence in probability for perturbed stochastic integral equations

  • Jean Picard1 

Probability Theory and Related Fields volume 81, pages 383–452 (1989)Cite this article

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Summary

In this work, one considers two stochastic integral equations indexed by some parameter ɛ and one studies the contiguity of their solutions when the parameter converges to some ε0. Two types of behaviour are described; they lead to the notion of regular and singular perturbations. The method which is used also enables a study of the rate of convergence. Applications to time discretization of equations are given.

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Authors and Affiliations

  1. INRIA, 2004, route des Lucioles, Sophia Antipolis, F-06565, Valbonne Cedex, France

    Jean Picard

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  1. Jean Picard
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Picard, J. Convergence in probability for perturbed stochastic integral equations. Probab. Th. Rel. Fields 81, 383–452 (1989). https://doi.org/10.1007/BF00340060

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  • Received: 04 July 1987

  • Revised: 26 May 1988

  • Issue Date: April 1989

  • DOI: https://doi.org/10.1007/BF00340060

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Keywords

  • Integral Equation
  • Stochastic Process
  • Probability Theory
  • Time Discretization
  • Statistical Theory
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