Record number :
Title of article :
Interpolation for partly hidden diffusion processes
Author/Authors :
Choi، نويسنده , , Changsun and Nam، نويسنده , , Dougu Nam، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2004
Pages :
From page :
To page :
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.
Keywords :
Interpolation , Hidden diffusion process , Backward boundary value problem , Last exit decomposition , Excursion
Journal title :
Stochastic Processes and their Applications
Journal title :
Stochastic Processes and their Applications
Serial Year :
Link To Document :