Related papers: Can time-homogeneous diffusions produce any distri…

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…

For a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, we study the joint distribution of the two local times $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ and $B(t)= \int_{0}^{t} d\tau \delta(X(\tau)-L) $ at…

We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and…

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master…

There is a natural connection between the class of diffusions, and a certain class of solutions to the Skorokhod Embedding Problem (SEP). We show that the important concept of minimality in the SEP leads to the new and useful concept of a…

We obtain uniform in time bounds for the solutions to a class of thermo-diffusive systems with classical and fractional diffusions. In the classical diffusion case, the nonlinearities are assumed to be at most exponentially growing, while…

A finite-time fluctuation theorem is proved for the diffusion-influenced surface reaction A<->B in a domain with any geometry where the species A and B undergo diffusive transport between the reservoir and the catalytic surface. A…

We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…

This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…

Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…

We consider a class of infinite-dimensional diffusions where the interaction between the components is both spatial and temporal. We start the system from a Gibbs measure with finite-range uniformly bounded interaction. Under suitable…

This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…

This paper is concerned with the inverse problem of determining the time and space dependent source term of diffusion equations with constant-order time-fractional derivative in $(0,2)$. We examine two different cases. In the first one, the…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…

In this paper, after a brief review of the general theory of dispersive waves in dissipative media, we present a complete discussion of the dispersion relations for both the ordinary and the time-fractional Cattaneo-Maxwell heat equations.…

We give optimal convergence rates in the central limit theorem for a large class of martingale difference sequences with bounded third moments. The rates depend on the behaviour of the conditional variances and for stationary sequences the…

We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…

In statistics on manifolds, the notion of the mean of a probability distribution becomes more involved than in a linear space. Several location statistics have been proposed, which reduce to the ordinary mean in Euclidean space. A…

This paper studies the large time behavior of aggregation-diffusion equations. For one spatial dimension with certain assumptions on the interaction potential, the diffusion index $m$, and the initial data, we prove the convergence to the…