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On finite difference schemes for degenerate stochastic parabolic partial differential equations

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Finite difference approximations in the space variable for possibly degenerate stochastic parabolic partial differential equations are investigated. Sharp estimates for the rate of convergence are obtained, and sufficient conditions are presented under which the speed of approximations can be accelerated to any given order of convergence by Richardson’s method. The main theorems generalize some results of the author with N. V. Krylov. Bibliography: 10 titles.

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Authors and Affiliations

  1. School of Mathematics and Maxwell Institute, University of Edinburgh King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom

    I. Gyöngy

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  1. I. Gyöngy
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Correspondence to I. Gyöngy.

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Dedicated to Professor N. V. Krylov on the occasion of his 70th birthday with gratitude and admiration

Translated from Problems in Mathematical Analysis 61, October 2011, pp. 87–108.

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Gyöngy, I. On finite difference schemes for degenerate stochastic parabolic partial differential equations. J Math Sci 179, 100–126 (2011). https://doi.org/10.1007/s10958-011-0584-3

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  • DOI: https://doi.org/10.1007/s10958-011-0584-3

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