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

Denis Villemonais 1
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : 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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Denis Villemonais. Uniform tightness for time-inhomogeneous particle systems and for conditional distributions of time-inhomogeneous diffusion processes. Markov Processes and Related Fields, Polymath, 2013, 19 (3), pp.543 - 562. ⟨hal-00681601⟩

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