Related papers: Large deviations for possibly reducible Markov cha…

We revisit classic ergodic large-deviation principles: for the occupation measure (Donsker-Varadhan), and for the empirical flux. We show that these problems can be embedded into a more general, discrete-time framework. A conditioning and…

Mostof the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…

In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…

Motivated by policy gradient methods in the context of reinforcement learning, we identify a large deviation rate function for the iterates generated by stochastic gradient descent for possibly non-convex objectives satisfying a…

We consider a family of Markov chains whose transition dynamics are affected by model parameters. Understanding the parametric dependence of (complex) performance measures of such Markov chains is often of significant interest. The…

We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past…

It is shown that irreducible two-state continuous-time Markov chains interacting on a network in a bilinear fashion have a unique stable steady state. The proof is elementary and uses the relative entropy function.

In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…

Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…

We study a class of dissipative PDE's perturbed by a bounded random kick force. It is assumed that the random force is non-degenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique…

Stochastic processes with random reinforced relocations have been introduced in the physics literature to model animal foraging behaviour. Such a process evolves as a Markov process, except at random relocation times, when it chooses a time…

This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…

We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…

We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…

We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…

It has been well known for some time that for strictly stationary Markov chains that are ``reversible'', that special symmetry provides special extra features in the mathematical theory. This paper here is primarily a purely expository…

In this paper, we consider a class of reflected stochastic differential equations for which the constraint is not on the paths of the solution but on its law. We establish a small noise large deviation principle, a large deviation for short…