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Teoriya Veroyatnostei i ee Primeneniya, 1995, Volume 40, Issue 3, Pages 657–665
(Mi tvp3464)
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This article is cited in 11 scientific papers (total in 11 papers)
Short Communications
Solution of the first boundary value problem for parabolic equations by integration of stochastic differential equations
G. N. Mil'shtein Ural State University
Abstract:
The solution of the general Dirichlet problem is connected in a well-known manner with a system of stochastic differential equations. The paper describes a number of methods of constructing a Markovian chain with absorbtion weakly approximating the system solutions so that the expectation of a certain functional in the chain trajectories is close to the solution of the original problem. For the examined methods the convergence theorems are established indicating the order of accuracy with respect to the size of approximation step.
Keywords:
numeric integration of stochastic differential equations, weak approximation of solution of stochastic differential equations, one-step accuracy order of a method, order of the method convergence, Monte Carlo methods of solution of mathematical physics problems.
Received: 10.11.1992
Citation:
G. N. Mil'shtein, “Solution of the first boundary value problem for parabolic equations by integration of stochastic differential equations”, Teor. Veroyatnost. i Primenen., 40:3 (1995), 657–665; Theory Probab. Appl., 40:3 (1995), 556–563
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https://www.mathnet.ru/eng/tvp3464 https://www.mathnet.ru/eng/tvp/v40/i3/p657
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Abstract page: | 399 | Full-text PDF : | 105 | First page: | 30 |
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