Interpolation for partly hidden diffusion processes

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Title
Interpolation for partly hidden diffusion processes
Author(s)
C Choi; DougU Nam
Bibliographic Citation
Stochastic Processes and Their Applications, vol. 113, no. 2, pp. 199-216
Publication Year
2004
Abstract
Let Xt be n-dimensional diffusion process and St be a smooth set-valued function. Suppose Xt is invisible when Xt∈St, but we can see the process exactly otherwise. Let Xt0 ∈St0 and we observe the process from the beginning till the signal reappears out of the obstacle after t0. With this information, we evaluate the estimators for the functionals of Xt on a time interval containing t0 where the signal is hidden. We solve related 3 PDEs in general cases. We give a generalized last exit decomposition for n-dimensional Brownian motion to evaluate its estimators. An alternative Monte Carlo method is also proposed for Brownian motion. We illustrate several examples and compare the solutions between those by the closed form result, finite difference method, and Monte Carlo simulations.
Keyword
backward boundary value problemexcursionhidden diffusion processinterpolationlast exit decomposition
ISSN
0304-4149
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.spa.2004.03.014
Type
Article
Appears in Collections:
1. Journal Articles > Journal Articles
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