Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion II∗

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

Asymptotic Behavior of Weighted Quadratic and Cubic Variations of Fractional Brownian Motion

The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H . In the quadratic (resp. cubic) case, when H < 1/4 (resp. H < 1/6), we show by means of Malliavin calculus that the convergence holds in L toward an explicit limit which only depends on B. This result is somewhat surprisi...

Asymptotic Behavior of Weighted Quadratic and Cubic Variations of Fractional Brownian Motion by Ivan Nourdin

The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H . In the quadratic (resp. cubic) case, when H < 1/4 (resp. H < 1/6), we show by means of Malliavin calculus that the convergence holds in L2 toward an explicit limit which only depends on B. This result is somewhat surpris...

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

The Effects of Different SDE Calculus on Dynamics of Nano-Aerosols Motion in Two Phase Flow Systems

Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...