Filtered Brownian motions as weak limit of filtered Poisson processes

Parameter Estimation for Multi-dimensional Filtered Poisson Processes

Information Processes in Filtered Experiments

In this paper we give explicit representations for Kullback-Leibler information numbers between a priori and a posteriori distributions, when the observations come from a semimartingale. We assume that the distribution of the observed semimartingale is described in terms of the so-called triplet of predictable characteristics. We end by considering the corresponding notions in a model with a fr...

Bayesian deconvolution of noisy filtered point processes

The detection and estimation of filtered point processes using noisy data is an essential requirement in many seismic, ultrasonic, and nuclear applications. In this paper, we address this joint detection/estimation problem using a Bayesian approach, which allows us to easily include any relevant prior information. Performing Bayesian inference for such a complex model is a challenging computati...

The Isolation Time of Poisson Brownian Motions

Let the nodes of a Poisson point process move independently in R according to Brownian motions. We study the isolation time for a target particle that is placed at the origin, namely how long it takes until there is no node of the Poisson point process within distance r of it. In the case when the target particle does not move, we obtain asymptotics for the tail probability which are tight up t...

Weak Convergence of Reflecting Brownian Motions

1. Introduction. We will show that if a sequence of domains D k increases to a domain D then the reflected Brownian motions in D k 's converge to the reflected Brownian motion in D, under mild technical assumptions. Our theorem follows easily from known results and is perhaps known as a " folk law " among the specialists but it does not seem to be recorded anywhere in an explicit form. The purp...