Related papers: Excursions Above the Minimum for Diffusions
In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our…
First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This modifies a formula by Perry et al (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for…
We consider the motion of an overdamped particle in a periodic potential lacking spatial symmetry under the influence of symmetric L\'evy noise, being a minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the L\'evy…
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of…
Let $x$ denote a diffusion process defined on a closed compact manifold. In an earlier article, the author introduced a new approach to constructing admissible vector fields on the associated space of paths, under the assumption of…
Probing the anomalous nanoscale intermixing using molecular dynamics (MD) simulations in Pt/Ti bilayer we reveal the superdiffusive nature of interfacial atomic transport. It is shown that the Pt atoms undergo anomalous atomic transport…
We introduce and study branching interval partition diffusions in their natural generality. We let interval widths evolve independently according to a general real-valued diffusion subject only to conditions that ensure finite lifetimes of…
In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by…
For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…
Path decomposition is performed to analyze the pre-supremum, post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy process taken up to an independent exponential time T as motivated by the aim of finding…
An obvious way to simulate a L\'evy process $X$ is to sample its increments over time $1/n$, thus constructing an approximating random walk $X^{(n)}$. This paper considers the error of such approximation after the two-sided reflection map…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
We study the statistics of encounters of L\'evy flights by introducing the concept of vicious L\'evy flights - distinct groups of walkers performing independent L\'evy flights with the process terminating upon the first encounter between…
We study transport in a one-dimensional lattice system with two conserved quantities -- `volume' and energy. Considering a slowly evolving local equilibrium state that is slightly deviated from an underlying global equilibrium, we estimate…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
Let $\tau(x)$ be the epoch of first entry into the interval $(x,\infty)$, $x>0$, of the reflected process $Y$ of a L\'evy process $X$, and define the overshoot $Z(x) = Y(\tau(x))-x$ and undershoot $z(x) = x - Y(\tau(x)-)$ of $Y$ at the…
In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds…
Diffusion, a ubiquitous phenomenon in nature, is a consequence of particle number conservation and locality, in systems with sufficient damping. In this paper we consider diffusive processes in the bulk of Weyl semimetals, which are exotic…
We consider a process $Z$ on the real line composed from a L\'evy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of $Z$ seen from its supremum, the supremum $\overline Z$…
The formal consideration of the concept of interaction in thermodynamic analysis makes it possible to deduce, in the broadest terms, new results related to the coevolution of interacting systems, irrespective of their distance from…