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This article is cited in 2 scientific papers (total in 2 papers)
On the distribution density of the first exit point of a diffusion process form a small neighborhood of its initial position
B. P. Harlamov Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Abstract:
Considering a diffusion process in a $d$-dimensional space, we study the distribution of the first exit point of a process from a small neighborhood of its initial state. A weak asymptotic expansion in terms of the small scale parameter is obtained for the density of the distribution. In the case of spherical neighborhoods, simple formulas are deduced for the first three coefficients of the expansion, reflecting the probabilistic sense of the coefficients of an elliptic partial differential equation.
Keywords:
diffusion process, first exit time, first exit point, partial differential equation, elliptic type, Green's function, integral equation, weak asymptotics of density.
Received: 25.07.1997 Revised: 23.06.1998
Citation:
B. P. Harlamov, “On the distribution density of the first exit point of a diffusion process form a small neighborhood of its initial position”, Teor. Veroyatnost. i Primenen., 45:3 (2000), 536–554; Theory Probab. Appl., 45:3 (2001), 450–465
Linking options:
https://www.mathnet.ru/eng/tvp484https://doi.org/10.4213/tvp484 https://www.mathnet.ru/eng/tvp/v45/i3/p536
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Abstract page: | 273 | Full-text PDF : | 141 | First page: | 12 |
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