Related papers: Long time behaviour of 1/2 H\"older diffusion popu…
Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an…
We examine the long time behaviour of A+B->0 reaction diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constants $D_A$, $D_B$, and initial…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
The transition from localized to systemic spreading of bacteria, viruses and other agents is a fundamental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple…
A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the…
This paper is concerned with stochastic processes that model multiple (or iterated) scattering in classical mechanical systems of billiard type, defined below. From a given (deterministic) system of billiard type, a random process with…
We consider a one-parameter family of invertible maps of a two-dimensional lattice, obtained by applying round-off to planar rotations. All orbits of these maps are conjectured to be periodic. We let the angle of rotation approach pi/2, and…
We consider an elliptic and time-inhomogeneous diffusion process with time-periodic coefficients evolving in a bounded domain of $\mathbb{R}^d$ with a smooth boundary. The process is killed when it hits the boundary of the domain (hard…
We investigate the diffusive motion of an overdamped classical particle in a 1D random potential using the mean first-passage time formalism and demonstrate the efficiency of this method in the investigation of the large-time dynamics of…
We prove that for harmonic quasiconformal mappings $\alpha$-H\"older continuity on the boundary implies $\alpha$-H\"older continuity of the map itself. Our result holds for the class of uniformly perfect bounded domains, in fact we can…
We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…
We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
We investigate the distribution properties of the fractional L\'evy motion. We consider separately the cases $0<H<1/2$ (short memory) and $1/2<H<1$ (long memory), where $H$ is the Hurst parameter, and present the asymptotic behaviour of the…
We provide a class of diffusion processes for continuous time-varying multivariate angular data with explicit transition probability densities, enabling exact likelihood inference. The presented diffusions are time-reversible and can be…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse…
In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost…
We describe the processes obtained by time reversal of a class of stationary jump-diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each…