Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111232
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dc.contributor.authorMilstein, G. N.en
dc.contributor.authorTretyakov, M. V.en
dc.date.accessioned2022-05-12T08:15:11Z-
dc.date.available2022-05-12T08:15:11Z-
dc.date.issued2003-
dc.identifier.citationMilstein G. N. The Simplest Random Walks for the Dirichlet Problem / G. N. Milstein, M. V. Tretyakov // Theory of Probability and its Applications. — 2003. — Vol. 47. — Iss. 1. — P. 53-68.en
dc.identifier.issn0040-585X-
dc.identifier.otherAll Open Access, Green3
dc.identifier.urihttp://hdl.handle.net/10995/111232-
dc.description.abstractThe Dirichlet problem for both parabolic and elliptic equations is considered. A solution of the corresponding characteristic system of stochastic differential equations is approximated in the weak sense by a Markov chain. If a state of the chain comes close to the boundary of the domain in which the problem is considered, then in the next step the chain either stops on the boundary or goes inside the domain with some probability due to an interpolation law. An approximate solution of the Dirichlet problem has the form of expectation of a functional of the chain trajectory. This makes it possible to use the Monte Carlo technique. The proposed methods are the simplest ones because they are based on the weak Euler approximation and linear interpolation. Convergence theorems, which give accuracy orders of the methods, are proved. Results of some numerical tests are presented.en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.rightsinfo:eu-repo/semantics/openAccessen
dc.sourceTheory Probab. Appl.2
dc.sourceTheory of Probability and its Applicationsen
dc.subjectDIRICHLET PROBLEM FOR PARABOLIC AND ELLIPTIC EQUATIONSen
dc.subjectMARKOV CHAINSen
dc.subjectPROBABILISTIC REPRESENTATIONSen
dc.subjectRANDOM WALKSen
dc.subjectWEAK APPROXIMATION OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONSen
dc.titleThe Simplest Random Walks for the Dirichlet Problemen
dc.typeArticleen
dc.typeinfo:eu-repo/semantics/articleen
dc.typeinfo:eu-repo/semantics/submittedVersionen
dc.identifier.scopus0037265529-
local.contributor.employeeMilstein, G.N., Department of Mathematics, Ural State University, Lenin St. 51, 620083 Ekaterinburg, Russian Federation, Weierstra-Inst. Angew. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany; Tretyakov, M.V., Inst. of Mathematics and Mechanics, Russian Academy of Sciences, S. Kovalevskaya St. 16, 620219 Ekaterinburg, Russian Federation, Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdomen
local.description.firstpage53-
local.description.lastpage68-
local.issue1-
local.volume47-
local.contributor.departmentDepartment of Mathematics, Ural State University, Lenin St. 51, 620083 Ekaterinburg, Russian Federation; Weierstra-Inst. Angew. Anal./S., Mohrenstr. 39, D-10117 Berlin, Germany; Inst. of Mathematics and Mechanics, Russian Academy of Sciences, S. Kovalevskaya St. 16, 620219 Ekaterinburg, Russian Federation; Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdomen
local.identifier.eid2-s2.0-0037265529-
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