Stochastic differential equations with critical drifts

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Stochastic Differential Equations with Jumps

Gradient estimates and a Harnack inequality are established for the semigroup associated to stochastic differential equations driven by Poisson processes. As applications, estimates of the transition probability density, the compactness and ultraboundedness of the semigroup are studied in terms of the corresponding invariant measure.

Stochastic Differential Equations with Applications

Stochastic differential equations with jumps,

This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions. Subject classifications: Primary 60H10; Secondary 60H30, 60J75

Stochastic Flows of Sdes with Irregular Drifts and Stochastic Transport Equations

Abstract. In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) drifts, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere stochastic invertible flow associated with the SDE in the sense of Lebesgue measure. In the case of constant diffusions and BV drifts, we obtain such a result...