Related papers: Sticky couplings of multidimensional diffusions wi…
In this paper we study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a…
The aim of this paper is to establish the existence and uniqueness of the solution to a system of nonlinear fully coupled forward-backward doubly stochastic differential equations with Poisson jumps. Our system is Markovian in the sense…
We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has positive Lebesgue measure with positive…
We present a novel idea for a coupling of solutions of stochastic differential equations driven by L\'{e}vy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential…
By using lower bound conditions of the L\'evy measure w.r.t. a nice reference measure, the coupling and strong Feller properties are investigated for the Markov semigroup associated with a class of linear SDEs driven by (non-cylindrical)…
We give a Dirichlet form approach for the construction of a distorted Brownian motion in $E:=[0,\infty)^n$, $n\in\mathbb{N}$, where the behavior on the boundary is determined by the competing effects of reflection from and pinning at the…
Gaw\c{e}dzki and Horvai have studied a model for the motion of particles carried in a turbulent fluid and shown that in a limiting regime with low levels of viscosity and molecular diffusivity, pairs of particles exhibit the phenomena of…
In this paper, we establish a general convergence theorem for solutions of multivariate stochastic differential equations with countably many singular terms expressed as integrals with respect to local times. The processes under…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
We present a coupling framework for Stokes-Darcy systems valid for arbitrary flow direction at low Reynolds numbers and for isotropic porous media. The proposed method is based on an overlapping domain decomposition concept to represent the…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
Attractiveness is a fundamental tool to study interacting particle systems and the basic coupling construction is a usual route to prove this property, as for instance in simple exclusion. The derived Markovian coupled process…
We study the optimal Markovian coupling problem for two Pi-valued Feller processes {X_t} and {Y_t}, which seeks a coupling process {(X_t, Y_t)} that minimizes the right derivative at t = 0 of the expected cost E^{(x,y)}[c(X_t, Y_t)], for…
We develop continuous time Markov chain (CTMC) approximation of one-dimensional diffusions with a lower sticky boundary. Approximate solutions to the action of the Feynman-Kac operator associated with a sticky diffusion and first passage…
The 1D Ising model is the simplest Hamiltonian-based model in statistical mechanics. The sim- plest interacting particle process is the Symmetric Exclusion Process (SEP), a 1D lattice gas of particles that hop symmetrically and cannot…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical…
We consider the Markov random flight $\bold X(t), \; t>0,$ in the three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$ and the uniform choice of the initial and each new direction at random time instants that form a…
We present a one-dimensional tight-binding chain of two-level systems coupled only through common dissipative Markovian reservoirs. This quantum chain can demonstrate anomalous thermodynamic behavior contradicting Fourier law. Population…
This work focuses on a class of regime-switching jump diffusion processes, which is a two component Markov processes $(X(t),\Lambda(t))$, where $\Lambda(t)$ is a component representing discrete events taking values in a countably infinite…