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Xi-Liang Fan

Publications and source records attributed to Xi-Liang Fan.

3 recordsLinked to original sources
arXiv2020

Moment estimates and applications for SDEs driven by fractional Brownian motion with irregular drifts

In this paper, high-order moment, even exponential moment, estimates are established for the Hölder norm of solutions to stochastic differential equations driven by fractional Brownian motion whose drifts are measurable and have linear growth. As applications, we first study the weak uniqueness of solutions to fractional stochastic differential equations. Moreover, combining our estimates and the Fourier transform, we establish the existence of density of solutions to equations with irregular drifts.

math.PR↗
arXiv2013

Harnack Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion

For stochastic differential equation driven by fractional Brownian motion with Hurst parameter $H>1/2$, Harnack type inequalities are established by constructing a coupling with unbounded time-dependent drift. These inequalities are applied to the study of existence and uniqueness of invariant measure for a discrete Markov semigroup constructed in terms of the distribution of the solution. Furthermore, we show that entropy-cost inequality holds for the invariant measure.

math.PR↗