Investigation of stochastic problems of mathematical physics
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 212-221
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The paper is devoted to constructing approximations of the Brownian motion in models leading to stochastic differential equations. For fundamental problems of mathematical physics, namely, for the problem of small vibrations of a string and the problem of heat conduction in a rod, approaches to defining and formalizing random perturbations are shown. For each of these problems, a sequence of random variables is constructed that converges in distribution to the Brownian motion describing random perturbations. The constructed approximations can be used for finding approximate solutions of stochastic problems.
Keywords:
Cauchy problem, Brownian motion, approximate solutions, continuous models, central limit theorem.
Mots-clés : binomial models
Mots-clés : binomial models
@article{TIMM_2012_18_2_a19,
author = {V. S. Parfenenkova},
title = {Investigation of stochastic problems of mathematical physics},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {212--221},
publisher = {mathdoc},
volume = {18},
number = {2},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a19/}
}
V. S. Parfenenkova. Investigation of stochastic problems of mathematical physics. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 212-221. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a19/