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

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2012-11-19 DOI:10.1080/17442508.2014.924937

C. Profeta, Abass Sagna

引用次数: 6

Abstract

We consider a model composed of a signal process X given by a classic stochastic differential equation and an observation process Y, which is supposed to be correlated to the signal process. We assume that 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>0. 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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用布朗桥法估计非线性滤波模型中的条件命中时间

我们考虑一个由经典随机微分方程给出的信号过程X和与信号过程相关的观测过程Y组成的模型。我们假设过程Y在离散时间从时间0到s>0被观察到，目的是在这些观察的条件下估计未观察到的过程X在给定时间t>0后越过固定障碍的概率。我们将此问题表述为一般的非线性滤波问题，并使用最优量化和蒙特卡罗模拟技术来估计所涉及的量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.