Filtering partially observable diffusions up to the exit time from a domain

N. V. Krylov; Teng Wang

doi:10.1016/j.spa.2011.04.008

Filtering partially observable diffusions up to the exit time from a domain

N. V. Krylov, Teng Wang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary.

Original language	English (US)
Pages (from-to)	1785-1815
Number of pages	31
Journal	Stochastic Processes and their Applications
Volume	121
Issue number	8
DOIs	https://doi.org/10.1016/j.spa.2011.04.008
State	Published - Aug 2011

Bibliographical note

Funding Information:
The work of the first author was partially supported by NSF Grant DMS-0653121 .

Keywords

Filtering equations in domains
Stochastic partial differential equations

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10.1016/j.spa.2011.04.008

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abstract = "We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary.",

keywords = "Filtering equations in domains, Stochastic partial differential equations",

author = "Krylov, \{N. V.\} and Teng Wang",

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AU - Wang, Teng

N1 - Funding Information: The work of the first author was partially supported by NSF Grant DMS-0653121 .

PY - 2011/8

Y1 - 2011/8

N2 - We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary.

AB - We consider a two-component diffusion process with the second component treated as the observations of the first one. The observations are available only until the first exit time of the first component from a fixed domain. We derive filtering equations for an unnormalized conditional distribution of the first component before it hits the boundary and give a formula for the conditional distribution of the first component at the first time it hits the boundary.

KW - Filtering equations in domains

KW - Stochastic partial differential equations

UR - https://www.scopus.com/pages/publications/79958133109

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M3 - Article

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SP - 1785

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 8

ER -

Filtering partially observable diffusions up to the exit time from a domain

Abstract

Bibliographical note

Keywords

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