Geodesic
On stochastic algorithms for solving boundary value problems for the Laplace operator
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 133-142

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the mixed boundary value problem for the Poisson equation. A random walk inside the domain are constructed and unbiased estimator for the solution of the boundary value problem defined on its trajectories. The finiteness of the estimator variance proved. The possibility of practical realization of the estimator by Monte Carlo method studied. 
@article{ZNSL_2015_442_a8,
     author = {A. S. Sipin},
     title = {On stochastic algorithms for solving boundary value problems for the {Laplace} operator},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {133--142},
     publisher = {mathdoc},
     volume = {442},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a8/}
}
TY  - JOUR
AU  - A. S. Sipin
TI  - On stochastic algorithms for solving boundary value problems for the Laplace operator
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 133
EP  - 142
VL  - 442
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a8/
LA  - ru
ID  - ZNSL_2015_442_a8
ER  - 
%0 Journal Article
%A A. S. Sipin
%T On stochastic algorithms for solving boundary value problems for the Laplace operator
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 133-142
%V 442
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a8/
%G ru
%F ZNSL_2015_442_a8
A. S. Sipin. On stochastic algorithms for solving boundary value problems for the Laplace operator. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 23, Tome 442 (2015), pp. 133-142. http://geodesic.mathdoc.fr/item/ZNSL_2015_442_a8/