Strong solutions to stochastic equations with a Lévy noise and a non-constant diffusion coefficient

V. Bogachev; Pilipenko A. Y.

doi:10.1134/S1064562416040244

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Strong solutions to stochastic equations with a Lévy noise and a non-constant diffusion coefficient

Doklady Mathematics. 2016. Vol. 94. No. 1. P. 438–440.

Bogachev V., Pilipenko A. Y.

The goal of this study is to prove an existence and uniqueness theorem for the solution of a stochastic differential equation with Lévy noise in the case where the drift coefficient can be discontinuous. Additionally, the differentiability of the solution with respect to the initial condition is proved.

Language: English

DOI

Keywords: stochastic equations Levy noise

Statistics of residence time for Lévy flights in unstable parabolic potentials

Kharcheva A. A., Dubkov A. A., Spagnolo B. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 P. 042142

We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average ...

Added: December 14, 2022