Conditional hitting time estimation in a nonlinear filtering model by the Brownian bridge method

2012/11/19 by Christophe Pofeta, Abass Sagna, Pofeta, Christophe +1
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Control Systems and Identification #Stochastic processes and financial applications #Target Tracking and Data Fusion in Sensor Networks #math.PR

paper · pdf · doi:10.48550/arxiv.1211.4553

arxiv created 2012/11/19 · arxiv updated 2012/11/20

Abstract

The model consists of a signal process X which is a general Brownian diffusion process and an observation process Y, also a diffusion process, which is supposed to be correlated to the signal process. We suppose that the process Y is observed from time 0 to s>0 at discrete times and aim to estimate, conditionally on these observations, the probability that the non-observed process X crosses a fixed barrier after a given time t>s. We formulate this problem as a usual nonlinear filtering problem and use optimal quantization and Monte Carlo simulations techniques to estimate the involved quantities.

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