Transience and Non-explosion of Certain Stochastic Newtonian Systems

Vassili N. Kolokoltsov (Nottingham Trent University)
R.L. Schilling (University of Sussex)
A. E. Tyukov (University of Sussex)

Abstract


We give sufficient conditions for non-explosion and transience of the solution $(x_t, p_t)$ (in dimensions $\geq 3$) to a stochastic Newtonian system of the form $$ \begin{cases} dx_t= p_t \, dt ,  \\ dp_t= -\frac{\partial V(x_t) }{\partial x} \, dt - \frac{ \partial c(x_t) }{ \partial x} \, d\xi_t , \end{cases} $$ where $\{\xi_t\}_{t\geq 0}$ is a $d$-dimensional L\'evy process, $d\xi_t$ is an It\^o differential and $c\in C^2(\mathbb{R}^d,\mathbb{R}^d)$, $V\in C^2(\mathbb{R}^d,\mathbb{R})$ such that $V\geq 0$.

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Pages: 1-19

Publication Date: October 2, 2002

DOI: 10.1214/EJP.v7-118

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