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Erschienen in:
1989 | OriginalPaper | Buchkapitel
Various Boundary Value Problems Related to the Laplace Operator
verfasst von : S. M. Ermakov, V. V. Nekrutkin, A. S. Sipin
Erschienen in: Random Processes for Classical Equations of Mathematical Physics
Verlag: Springer Netherlands
Enthalten in: Professional Book Archive
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This Chapter describes the construction of Markov chains and estimators for the solution of concrete boundary value problems connected with the Laplace operator. The main difficulty to be overcome is the obtaining of an integral equation equivalent to a given problem and then choosing a Markov chain on whose trajectories unbiased estimators are to be constructed. For various problems associated with the Laplace operator the difficulty is overcome with the help of a corresponding Green formula.