Related papers: Exit-problem for a class of non-Markov processes w…
We study the exit problem of solutions of the stochastic differential equation dX(t)=-U'(X(t))dt+epsilon dL(t) from bounded or unbounded intervals which contain the unique asymptotically stable critical point of the deterministic dynamical…
The paper analyses the sensitivity of the finite time horizon boundary non-crossing probability $F(g)$ of a general time-inhomogeneous diffusion process to perturbations of the boundary $g$. We prove that, for boundaries $g\in C^2,$ this…
The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…
In this paper we characterize the distribution of the first exit time from an arbitrary open set for a class of semi-Markov processes obtained as time-changed Markov processes. We estimate the asymptotic behaviour of the survival function…
The fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…
In this paper, under some appropriate assumptions, we prove the existence of the minimal time-dependent pullback $\mathcal D_{\sigma}^{\mathcal{H}_{t}}$-attractors ${\mathcal{A}}_{\mathcal D_{\sigma}^{\mathcal{H}_{t}}}$ for the…
We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…
We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…
We consider a two-dimensional Hamiltonian system perturbed by a small diffusion term, whose coefficient is state-dependent and non-degenerate. As a result, the process consists of the fast motion along the level curves and slow motion…
This paper investigates a diffusion process in a narrow tubular domain with reflecting boundary conditions, where the geometry serves as a singular perturbation of an underlying graph in $\mathbb{R}^2$ or $\mathbb{R}^3$. The construction…
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more…
We give a new proof of the vanishing noise limit theorem for exit times of 1-dimensional diffusions conditioned on exiting through a point separated from the starting point by a potential wall. We also prove a scaling limit for exit…
We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous…
We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a…
In this note, we connect two seemingly unrelated objects: On the one hand is a two-dimensional drift-diffusion process $X$ with divergence-free and time-independent drift $b$. The drift is given by a stationary Gaussian ensemble, and we…
We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic…
We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the…
We consider processes that coincide with a given diffusion process outside a finite collection of domains. In each of the domains, there is, additionally, a large drift directed towards the interior of the domain. We describe the limiting…
The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…
In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of…