Abstract
As has been pointed out in Section 1.3, one of the ways to solve the first boundary problem is to reduce it to the integral equation satisfying appropriate conditions and to construct an unbiased estimator of its solution on the trajectories of the convergent Markov chain adapted to this integral equation. In Section 1.3 the scheme was realized for the simplest example of the interior Dirichlet problem for the Laplace operator. Here a more complicated and interesting case of an arbitrary elliptic operator with smooth coefficients will be considered.
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© 1989 Kluwer Academic Publishers
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Ermakov, S.M., Nekrutkin, V.V., Sipin, A.S. (1989). First Boundary Value Problem for the Equation of the Elliptic Type. In: Random Processes for Classical Equations of Mathematical Physics. Mathematics and its Applications (Soviet Series), vol 34. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2243-3_2
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DOI: https://doi.org/10.1007/978-94-009-2243-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7504-6
Online ISBN: 978-94-009-2243-3
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