We consider a filtering problem when the state process is a reflected Brownian motion X-t and the observation process is its local time A(s), for s <= t. For this model we derive an approximation scheme based on a suitable interpolation of the observation process A(t). 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 Azema martingale. (C) 2006 Elsevier B.V. All rights reserved.
Nappo, G., Torti, B. (2006). Filtering of a reflected Brownian motion with respect to its local time. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 116(4), 568-584 [10.1016/j.spa.2005.12.007].
Filtering of a reflected Brownian motion with respect to its local time
TORTI, BARBARA
2006-01-01
Abstract
We consider a filtering problem when the state process is a reflected Brownian motion X-t and the observation process is its local time A(s), for s <= t. For this model we derive an approximation scheme based on a suitable interpolation of the observation process A(t). 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 Azema martingale. (C) 2006 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
