Uniform tightness for time-inhomogeneous particle systems and for conditional distributions of time-inhomogeneous diffusion processes

Details Uniform tightness for time-inhomogeneous particle systems and for conditional distributions of time-inhomogeneous diffusion processes Uniform tightness for time-inhomogeneous particle systems and for conditional distributions of time-inhomogeneous diffusion processes

2012-03-21

arxiv.org/abs/1203.4825v1

Mathematics

Probability

20 pages

Scientific paper

In this article, we consider time-inhomogeneous diffusive particle systems, whose particles jump from the boundary of a bounded open subset of $\R^d$, $d\geq 1$. We give a sufficient criterion for the family of empirical distributions of such systems to be uniformly tight, independently of the jump location of the particles. As an application, we show that the conditional distribution of a family of time-inhomogeneous and environment-dependent diffusions conditioned not to hit the boundary of a bounded open subset of $\R^d$ is uniformly tight.

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