Related papers: Inhomogeneous exponential jump model
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of L\'evy-driven type…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…
In this paper we consider the stochastic six-vertex model on a cylinder with arbitrary initial data. First, we show that it exhibits a limit shape in the thermodynamic limit, whose density profile is given by the entropy solution to an…
We study by numerical simulations the two-dimensional Inelastic Maxwell Model (IMM), and show how the inelasticity of collisions together with the fluctuations of the number of collisions undergone by a particle lead to energy fluctuations…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
This paper discusses tractable development and statistical estimation of a continuous time stochastic process with a finite state space having non-Markov property. The process is formed by a finite mixture of right-continuous Markov jump…
We study the exact fluctuating hydrodynamics of the scaled Light-Heavy model (sLH), in which two species of particles (light and heavy) interact with a fluctuating surface. This model is similar in definition to the unscaled Light-Heavy…
In this paper, we study the long-time behavior of a fluid particle immersed in a turbulent fluid driven by a diffusion with jumps, that is, a Feller process associated with a non-local operator. We derive the law of large numbers and…
Stochastic processes of interacting particles with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
Various lattice gas automata have been proposed in the past decades to simulate physics and address a host of problems on collective dynamics arising in diverse fields. In this work, we employ the lattice gas model defined on the sphere to…
We introduce a general variational framework to address the tunneling of hot Fermi systems. We use the representation of the trace of the imaginary time $\tau=it$ propagator as a functional integral type of a sum over complete sets of…
Non-Hermitian topological edge states have many intriguing properties, but have so far mainly been discussed in terms of bulk-boundary correspondence. Here we propose to use a bulk property of diffusion coefficients for probing the…
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental…
The diffusive dynamics of a particle in a medium with space-dependent friction coefficient is studied within the framework of the inertial Langevin equation. In this description, the ambiguous interpretation of the stochastic integral,…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
In this work, we focus on an infinite horizon mean-field linear-quadratic stochastic control problem with jumps. Firstly, the infinite horizon linear mean-field stochastic differential equations and backward stochastic differential…
We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…