Related papers: Regularity of transition densities and ergodicity …
In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…
This paper provides necessary and sufficient conditions for exponential stabilization of distributed systems affine in control, evolving in a Banach state space, by means of constant controls. An explicit estimate of the convergence speed…
We show the existence of a broad class of affine Markov processes in the cone of positive self-adjoint Hilbert-Schmidt operators. Such processes are well-suited as infinite dimensional stochastic volatility models. The class of processes we…
In this paper, we introduce a new method of sampling from transition densities of diffusion processes including those unknown in closed forms by solving a partial differential equation satisfied by the quotient of transition densities. We…
In this paper we study time-inhomogeneous affine processes beyond the common assumption of stochastic continuity. In this setting times of jumps can be both inaccessible and predictable. To this end we develop a general theory of finite…
We establish strong Feller property and irreducibility for the transition semigroup associated to a class of nonlinear stochastic partial differential equations with multiplicative degenerate noise. As a by-product, we prove uniqueness of…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
We find necessary and sufficient conditions for a finite $K$-bi-invariant measure on a compact Gelfand pair $(G, K)$ to have a square-integrable density. For convolution semigroups, this is equivalent to having a continuous density in…
Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions consisting of continuous and discrete components. Novel…
The principle of permanence of large eddies is one of the central pillars onto which our understanding of decaying homogeneous turbulence is built. The validity conditions of this principle have been thoroughly discussed for constant…
Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long…
Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Using elliptic and parabolic regularity results in $L^p$-spaces and generalized Dirichlet form theory, we construct for every starting point weak solutions to SDEs in $\mathbb{R}^d$ up to their explosion times including the following…
We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion satisfies a stochastic differential equation (SDE) on $\mathbf{R}^d$…
Characterizing time-evolution of allele frequencies in a population is a fundamental problem in population genetics. In the Wright-Fisher diffusion, such dynamics is captured by the transition density function, which satisfies well-known…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…
This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…