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Infinite-dimensional Langevin equations: uniqueness and rate of convergence for finite-dimensional approximations
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  • Published: June 2001

Infinite-dimensional Langevin equations: uniqueness and rate of convergence for finite-dimensional approximations

  • Sigurd Assing1 

Probability Theory and Related Fields volume 120, pages 143–167 (2001)Cite this article

Abstract.

The paper deals with the infinite-dimensional stochastic equation dX= B(t, X) dt + dW driven by a Wiener process which may also cover stochastic partial differential equations. We study a certain finite dimensional approximation of B(t, X) and give a qualitative bound for its rate of convergence to be high enough to ensure the weak uniqueness for solutions of our equation. Examples are given demonstrating the force of the new condition.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany. e-mail: assing@mathematik.uni-bielefeld.de, , , , , , DE

    Sigurd Assing

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  1. Sigurd Assing
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Received: 6 November 1999 / Revised version: 21 August 2000 / Published online: 6 April 2001

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Assing, S. Infinite-dimensional Langevin equations: uniqueness and rate of convergence for finite-dimensional approximations. Probab Theory Relat Fields 120, 143–167 (2001). https://doi.org/10.1007/PL00008778

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  • Issue Date: June 2001

  • DOI: https://doi.org/10.1007/PL00008778

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  • Mathematics Subject Classification (2000): 60G30, 60H15
  • Key words or phrases: Stochastic partial differential equation – Girsanov theorem – Weak uniqueness – Martingale problem
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