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A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a...
We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ∈ (0, 1). We establish a diffusive homogenization limit for the tracer when th...
In the paper, the Bismut derivative formula is established for multidimensional SDEs driven by additive fractional noise ($1/2and moreover the Harnack inequality is given. Through a Lamperti t...
We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles ...
Individual movements of a rod-like self-propelled particle on a flat substrate are quantified. Biological systems that fit into this description may be the Gram-negative delta-proteobacterium Myxococc...
This paper is devoted to the construction of a solution for the "Inhomogenous skew Brownian motion" equation, which first appeared in a seminal paper by Sophie Weinryb, and recently, studied by \'{E}t...
Abstract: In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary ...
Abstract: We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but ...
Abstract: Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u...
Abstract: In this paper we consider the Stochastic isothermal, nonlinear, incompressible bipolar viscous fluids driven by a genuine cylindrical fractional Bronwnian motion with Hurst parameter $H \in ...
Abstract: This article is devoted to the construction of a solution for the "skew inhomogeneous Brownian motion" equation, which first appear in a seminal paper by Sophie Weinryb (1983). We investigat...
Abstract: Consider a $d$-dimensional Brownian motion in a random potential defined by attaching a non-negative and polynomially decaying potential around Poisson points. We introduce a repulsive inter...
Abstract: This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here for both point-to-point and point-to-plane model ...
Abstract: We present an extension of the Edwards model for conformations of individual chain molecules in solvents in terms of fractional Brownian motion, and discuss the excluded volume effect on the...
Firstly, we compute the distribution function for the hitting time of a linear time-dependent boundary t 7→ a + bt, a ≥ 0, b ∈ R, by a reflecting Brownian motion.

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