Related papers: Fractional Diffusion Bridges

Fractional Brownian motion (fBm) is an important scale-invariant Gaussian non-Markovian process with stationary increments, which serves as a prototypical example of a system with long-range temporal correlations and anomalous diffusion.…

We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…

Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation…

Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…

This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…

This article is devoted to study stochastic lattice dynamical systems driven by a fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. First of all, we investigate the existence and uniqueness of pathwise mild solutions to such…

Let alpha,T>0. We study the asymptotic properties of a least squares estimator for the parameter alpha of a fractional bridge defined as dX_t=-alpha*X_t/(T-t)dt+dB_t, with t in [0,T) and where B is a fractional Brownian motion of Hurst…

Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…

We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…

This paper is concerned with transition paths within the framework of the overdamped Langevin dynamics model of chemical reactions. We aim to give an efficient description of typical transition paths in the small temperature regime. We…

This paper investigates the probability distribution of solutions to McKean--Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst parameter H>1/2. Our main contribution is the derivation of the associated…

In this article, we give some existence and smoothness results for the law of the solution to a stochastic heat equation driven by a finite dimensional fractional Brownian motion with Hurst parameter $H>1/2$. Our results rely on recent…

We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric…

In this paper, we introduce some fundamental notions related to the so-called stochastic derivatives with respect to a given $\sigma$-field $\mathcal{Q}$. In our framework, we recall well-known results about Markov--Wiener diffusions. We…

Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $H\in [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical…

We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter $\hat{\cal H} \in ( 1/2, 1)$. Using fixed point techniques, a…

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is…

The goal of this paper is to supplement the large deviation principle of the Freidlin--Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem kind. We describe a class of situations where…