Distribution dependent SDEs driven by additive fractional Brownian motion

Ergodicity of hypoelliptic SDEs driven by fractional Brownian motion

We demonstrate that stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter H > 1 2 have similar ergodic properties as SDEs driven by standard Brownian motion. The focus in this article is on hypoelliptic systems satisfying Hörmander’s condition. We show that such systems satisfy a suitable version of the strong Feller property and we conclude that the...

A Milstein-type scheme without Levy area terms for SDEs driven by fractional Brownian motion

In this article, we study the numerical approximation of stochastic differential equations driven by a multidimensional fractional Brownian motion (fBm) with Hurst parameter greater than 1/3. We introduce an implementable scheme for these equations, which is based on a second order Taylor expansion, where the usual Lévy area terms are replaced by products of increments of the driving fBm. The c...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

existence and measurability of the solution of the stochastic differential equations driven by fractional brownian motion

Flow properties of differential equations driven by fractional Brownian motion

We prove that solutions of stochastic differential equations driven by fractional Brownian motion for H > 1/2 define flows of homeomorphisms on R. AMS Subject Classification: 60H05, 60H07