Related papers: Stability of densities for perturbed Diffusions an…

We investigate stability of invariant measures of diffusion processes with respect to $L^p$ distances on the coefficients, under an assumption of log-concavity. The method is a variant of a technique introduced by Crippa and De Lellis to…

In this paper a new dissimilarity measure to identify groups of assets dynamics is proposed. The underlying generating process is assumed to be a diffusion process solution of stochastic differential equations and observed at discrete time.…

Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…

The problem of a particle diffusion in a fluctuating scalar field is studied. In contrast to most studies of advection diffusion in random fields we analyze the case where the particle position is also coupled to the dynamics of the field.…

In this paper a new estimator for the transition density $\pi$ of an homogeneous Markov chain is considered. We introduce an original contrast derived from regression framework and we use a model selection method to estimate $\pi$ under…

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…

Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…

We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes…

We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…

Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…

The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence…

We study the following model of hidden Markov chain: $Y_i=X_i+\epsilon_i$, $ i=1,...,n+1$ with $(X_i)$ a real-valued positive recurrent and stationary Markov chain and $(\epsilon_i)_{1\leq i\leq n+1}$ a noise independent of the sequence…

Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and…

We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…

We consider diffusion processes with the help of Markov random walk models. Especially the process of diffusion of a relativistic particle in a relativistic equilibrium system is considered. We interpret one of the results as causal Zeno…

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…

In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…

On the basis of perturbed Kolmogorov backward equations and path integral representation, we unify the derivations of the linear response theory and transient fluctuation theorems for continuous diffusion processes from a backward point of…

We study the kernel estimator of the transition density of bifurcating Markov chains. Under some ergodic and regularity properties, we prove that this estimator is consistent and asymptotically normal. Next, in the numerical studies, we…