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Transience and Non-explosion of Certain Stochastic Newtonian Systems

   
@article{EJP118,
	author = {Vassili Kolokoltsov and R.L. Schilling and A. Tyukov},
	title = {Transience and Non-explosion of Certain Stochastic Newtonian Systems},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {7},
	year = {2002},
	keywords = {Stochastic Newtonian systems; Levy processes; alpha-stable Levy processes; Transience; Non-explosion.},
	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 $V\geq 0$.},
	pages = {no. 19, 1-19},
	issn = {1083-6489},
	doi = {10.1214/EJP.v7-118},    
        url = {http://ejp.ejpecp.org/article/view/118}}