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Policy gradient methods are among the most effective methods in challenging reinforcement learning problems with large state and/or action spaces. However, little is known about even their most basic theoretical convergence properties,…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
The filtering of a Markov diffusion process on a manifold from counting process observations leads to `large' changes in the conditional distribution upon an observed event, corresponding to a multiplication of the density by the intensity…
We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…
In this paper we analyze the probability of consistency of sensor data distribution systems (SDDS), and determine suitable evaluation models. This problem is typically difficult, since a reliable model taking into account all parameters and…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…
Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…
This paper considers a distributed stochastic optimization problem where the goal is to minimize the time average of a cost function subject to a set of constraints on the time averages of a related stochastic processes called penalties. We…
In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the stationary distribution. With the help of MA structure and…
We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most…
In a first part, we prove a Lyapunov-type criterion for the $\xi\_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second…
This paper proposes an algorithm capable of driving a system to follow a piecewise linear trajectory without prior knowledge of the system dynamics. Motivated by a critical failure scenario in which a system can experience an abrupt change…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…
We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the…
New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…