Related papers: Moderate Deviation Principles for Unbounded Additi…

Constrained Markov Decision Processes (CMDPs) are notably more complex to solve than standard MDPs due to the absence of universally optimal policies across all initial state distributions. This necessitates re-solving the CMDP whenever the…

Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large…

Relative Divergence (RD) and Maximum Relative Divergence Principle (MRDP) for grading (order-comonotonic) functions (GF) on posets are used as an expression of Insufficient Reason Principle under the given prior information (IRP+). Classic…

Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…

The moderate deviation regime is concerned with the finite block length trade-off between communication cost and error for information processing tasks in the asymptotic regime, where the communication cost approaches a capacity-like…

Consider stochastic partial differential equations (SPDEs) with fully local monotone coefficients in a Gelfand triple $V\subseteq H\subseteq V^*$ $$ \left\{ \begin{align} &dX_t=A(t,X_t)dt+B(t,X_t)dW_t,\ t\in (0,T]\\\\& X_0=x\in H,…

We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…

The main goal of this article is to study the effect of small, highly nonlinear, unbounded drifts (small time large deviation principle (LDP) based on exponential equivalence arguments) for a class of stochastic partial differential…

Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

We consider non-standard Markov Decision Processes (MDPs) where the target function is not only a simple expectation of the accumulated reward. Instead, we consider rather general functionals of the joint distribution of terminal state and…

We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…

In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. [2009. The stochastic…

We prove sample path moderate deviation principles (MDP) for the current and the tagged particle in the symmetric simple exclusion process, which extends the results in \cite{xue2023moderate}, where the MDP was only proved at any fixed…

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…

Mean-field backward doubly stochastic differential equations (MF-BDSDEs, for short) are introduced and studied. The existence and uniqueness of solutions for MF-BDSDEs is established. One probabilistic interpretation for the solutions to a…

We study the weakly asymmetric simple exclusion process on the integer lattice. Under suitable constraints on the strength of the weak asymmetry of the dynamics, we prove moderate deviation principles for the fluctuation fields when the…

We study a class of infinite-horizon average-cost Markov Decision Processes (MDPs) whose reward and transition structures are nearly separable. For the totally separable baseline (that is, with no perturbation), we derive an explicit…

In this work, we investigate the Central Limit Theorem (CLT) and Moderate Deviation Principle (MDP) for the stochastic generalized Burgers-Huxley (SGBH) equation with multiplicative Gaussian noise. The SGBH equation is a…

A discrepancy principle for solving nonlinear equations with monotone operators given noisy data is formulated. The existence and uniqueness of the corresponding regularization parameter $a(\delta)$ is proved. Convergence of the solution…

This paper studies discrete-time average-cost infinite-horizon Markov decision processes (MDPs) with Borel state and action sets. It introduces new sufficient conditions for { the} validity of optimality inequalities and optimality…