相关论文: A reverse ergodic theorem for inhomogeneous killed…

Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to math finance, and under general stability conditions, it has a unique stationary distribution.…

It is shown that in systems with time-dependent and/or spatially nonuniform temperature $T(t,x)$, (i) most of the transport processes is weakly non-ergodic, and (ii) the diffusion (Brownian motion, BM) is anomalous. A few examples of simple…

We provide a criterion for establishing lower bounds on the rate of convergence in $f$-variation of a continuous-time ergodic Markov process to its invariant measure. The criterion consists of novel super- and submartingale conditions for…

The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected L\'evy processes. Like a Brownian motion, which is a weak limit of random walks,…

We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…

We revisit the ergodic theorem for the frontier of branching Brownian motion (BBM). Motivated by the proof of Arguin, Bovier, and Kistler \cite{arguin2012ergodic}, we provide a shorter and more direct argument. It relies on two…

We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in $\mathbb{R}^d$, which may be recurrent in any dimension. The limit $\mathcal{X}$ is an elliptic martingale diffusion, which may be…

We consider ergodic backward stochastic differential equations, in a setting where noise is generated by a countable state uniformly ergodic Markov chain. We show that for Lipschitz drivers such that a comparison theorem holds, these…

After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of…

We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective…

We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning the related counting process, and ergodic-type ones,…

We study an inverse scattering problem for a generic hyperbolic system of equations with an unknown coefficient called the reflectivity. The solution of the system models waves (sound, electromagnetic or elastic), and the reflectivity…

We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…

In this paper, we study branching Brownian motion with absorption, in which particles undergo Brownian motions and are killed upon hitting the absorption barrier. We prove that the empirical distribution function of the maximum of this…

In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove…

We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…

We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift-diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and…