Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156368 | Stochastic Processes and their Applications | 2006 | 17 Pages |
Abstract
We consider a filtering problem when the state process is a reflected Brownian motion Xt and the observation process is its local time Îs, for sâ¤t. For this model we derive an approximation scheme based on a suitable interpolation of the observation process Ît. The convergence of the approximating filter to the original one combined with an explicit construction of the approximating filter allows us to derive the explicit form of the original filter. The last result can be obtained also by means of the Azéma martingale.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Giovanna Nappo, Barbara Torti,