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 (in dimensions d greater or equal 3) of the solution
(x(t),p(t))
to a stochastic Newtonian system of the form
dx(t) = p(t) dt
dp(t) = DV(x(t))
dt − Dc(x(t))
dz(t)
where z(t) is a d-dimensional Levy process,
dz(t)
is an Ito differential, c is a
C2(Rd,
Rd) function and V a non-negative
C2(Rd, R) function
(with x-derivatives
denoted by Dc and DV).
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