Discrete-Time Langevin Motion in a Gibbs Potential
Applied Mathematics-a Journal of Chinese Universities Series B(2012)
摘要
We
consider a multivariate Langevin equation in discrete time, driven by a force
induced by certain Gibbs’states. The main goal of the paper is to study
the asymptotic behavior of a random walk with stationary increments (which are
interpreted as discrete-time speed terms) satisfying the Langevin equation. We
observe that (stable) functional limit theorems and laws of iterated logarithm
for regular random walks with i.i.d. heavy-tailed increments can be carried
over to the motion of the Langevin particle.
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