Geodesic
On the variance of the estimate of the functional of the diffusion process in a domain with a reflecting boundary
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 359-369

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The estimation of the functional of the diffusion process in a domain with a reflecting boundary, which is obtained on the basis of numerical modeling of its trajectories, is considered. The value of this functional coincides with the solution at a given point of a boundary value problem of the third kind for a parabolic equation. A formula is obtained for the limiting value of the variance of this estimate under decreasing step in the Euler method. To reduce the variance of the estimate, a transformation of the boundary value problem is used, similar to the one that was previously proposed in the case of an absorbing boundary. 
@article{SJVM_2022_25_4_a1,
     author = {S. A. Gusev},
     title = {On the variance of the estimate of the functional of the diffusion process in a domain with a reflecting boundary},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {359--369},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a1/}
}
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S. A. Gusev. On the variance of the estimate of the functional of the diffusion process in a domain with a reflecting boundary. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 25 (2022) no. 4, pp. 359-369. http://geodesic.mathdoc.fr/item/SJVM_2022_25_4_a1/