Related papers: Small time asymptotics of diffusion processes

In this paper, we are concerned with the asymptotic behavior of weak solutions to certain elliptic and parabolic problems involving the fractional $p$-Laplacian in cylindrical domains that become unbounded in one direction. The nonlocal…

We are considering the asimptotic behavior as $t\to\infty$ of solutions of the Cauchy problem for parabolic second order equations with time periodic coefficients. The problem is reduced to considering degenerate time-homogeneous diffusion…

Let $D\subset R^d$ be a bounded domain and denote by $\mathcal P(D)$ the space of probability measures on $D$. Let \begin{equation*} L=\frac12\nabla\cdot a\nabla +b\nabla \end{equation*} be a second order elliptic operator. Let…

This paper completes and partially improves some of the results of [arXiv:0809.5002] about the asymptotic behavior of solutions of linear and nonlinear elliptic equations with singular coefficients via an Almgren type monotonicity formula

Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these…

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition densities are proved. The observation time [0,T] may be fixed or lim n T = 0, where nh = T and h is a mesh…

We consider classes of diffeomorphisms of Euclidean space with partial asymptotic expansions at infinity; the remainder term lies in a weighted Sobolev space whose properties at infinity fit with the desired application. We show that two…

We study the small-time asymptotics for hypoelliptic diffusion processes conditioned by their initial and final positions, in a model class of diffusions satisfying a weak H\"ormander condition where the diffusivity is constant and the…

We consider a singularly perturbed Dirichlet spectral problem for an elliptic operator of second order. The coefficients of the operator are assumed to be locally periodic and oscillating in the scale $\varepsilon$. We describe the leading…

We consider time-changed diffusions driven by generators with discontinuous coefficients. The PDE's connections are investigated and in particular some results on the asymptotic analysis according to the behaviour of the coefficients are…

We prove that certain asymptotic moments exist for some random distance expanding dynamical systems and Markov chains in random dynamical environment, and compute them in terms of the derivatives at the $0$ of an appropriate pressure…

We consider a porous medium equation with nonlocal diffusion effects given by an inverse fractional Laplacian operator. In a previous paper we have found mass-preserving, nonnegative weak solutions of the equation satisfying energy…

We consider a time inhomogeneous strong Markov process $(\xi_t)_{t\ge 0}$ taking values in a Polish state space whose semigroup has a $T$-periodic structure. We give simple conditions which imply ergodicity of the grid chain…

We study transport processes on infinite networks. The solution of these processes can be modeled by an operator semigroup on a suitable Banach space. Classically, such semigroups are strongly continuous and therefore their asymptotic…

In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…

For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…

The short-time asymptotic behavior of the transition density function of the diffusion process generated by the general Grushin operator will be investigated, by using its explicit expression in terms of expectation. Further the dependence…

This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose the time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded…

For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…

In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a…