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Optimal estimation of diffusion processes hidden by general obstacles

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Hyung Geun Kim  and
Dougu Nam
Hyung Geun Kim*
Affiliation:
KAIST
Dougu Nam*
Affiliation:
KAIST
*
∗ Postal address: Division of Mathematics, KAIST, Taejon 305–701, Republic of Korea.
∗∗ Postal address: Division of Applied Mathematics, KAIST, Taejon 305–701, Republic of Korea. Email address: dunam@amath.kaist.ac.kr
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Abstract

Let Xt be an n-dimensional diffusion process and S(t) be a set-valued function. Suppose Xt is invisible when it is hidden by S(t), but we can see the process exactly otherwise. In this paper, we derive the optimal estimator E[f(X1) | Xs1Xs∉S(s), 0 ≤ s ≤ 1] for a bounded Borel function f. We illustrate some computations for Gauss-Markov processes.

Keywords

Optimal estimationreverse-time processlast-exit timeset-valued function

MSC classification

Primary: 60G35: Signal detection and filtering
Secondary: 60J60: Diffusion processes 60J65: Brownian motion
Type
Short Communications
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 1067 - 1073
Copyright
Copyright © by the Applied Probability Trust 2001 

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Footnotes

The second author is supported by BK 21 program.

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