相关论文: Chains with complete connections: General theory, …

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…

A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…

We study the stochastic 3D primitive equations of the atmospheric mechanics. We consider them under a bounded and non-degenerate noise, which is statistically periodic in time with period $1$. In such a case we prove that the associated…

The notion of a successful coupling of Markov processes, based on the idea that both components of the coupled system ``intersect'' in finite time with probability one, is extended to cover situations when the coupling is unnecessarily…

In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincar\'e recurrences…

This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…

We formalize and analyze the notions of stochastic monotonicity and realizable mono-tonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions…

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…

In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…

We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…

Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…

We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second,…

Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent…

The spatial symmetry property of truncated birth-death processes studied in Di Crescenzo [6] is extended to a wider family of continuous-time Markov chains. We show that it yields simple expressions for first-passage-time densities and…

In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas…

Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a…

A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…

We consider a general multivariate affine stochastic recursion and the associated Markov chain on $\mathbb R^{d}$. We assume a natural geometric condition which implies existence of an unbounded stationary solution and we show that the…

We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax…