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We analyse quantile temporal-difference learning (QTD), a distributional reinforcement learning algorithm that has proven to be a key component in several successful large-scale applications of reinforcement learning. Despite these…
We address the long time behaviour of weakly interacting diffusive particle systems on the d-dimensional torus. Our main result is to show that, under certain regularity conditions, the weak error between the empirical distribution of the…
In this paper, the tunnelling of a particle through a potential barrier is investigated in the presence of a time-dependent perturbation. The latter is attributed to the process of the energy measurement of the scattered particle. The…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…
From the data analysis we defined distribution function against the population on the level of various structure units, namely regions, federal districts and the country on the whole. We have studied peculiarities of the distribution…
The present paper is devoted to the investigation of the long term behavior of a class of singular multi-dimensional diffusion processes that get absorbed in finite time with probability one. Our focus is on the analysis of quasi-stationary…
Motion of particles (bodies) in presence of random effects can be considered stochastic process. However, application of widely known stochastic processes used for description of particle motion is reduced to relatively small class of…
We study the time evolution of thermodynamic observables that characterise the dissipative nature of thermal relaxation after an instantaneous temperature quench. Combining tools from stochastic thermodynamics and large-deviation theory, we…
We derive expressions for the first three moments of the decision time (DT) distribution produced via first threshold crossings by sample paths of a drift-diffusion equation. The "pure" and "extended" diffusion processes are widely used to…
In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the…
We investigate the work fluctuations in an overdamped non-equilibrium process that is stopped at a stochastic time. The latter is characterized by a first passage event that marks the completion of the non-equilibrium process. In…
We present a derivation of a recently proposed theory for the time dependence of density fluctuations in stationary states of strongly interacting, athermal, self-propelled particles. The derivation consists of two steps. First, we start…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
Variational time integrators are derived in the context of discrete mechanical systems. In this area, the governing equations for the motion of the mechanical system are built following two steps: (a) Postulating a discrete action; (b)…
From a logic point of view this is the third in the series to solve the problem of absence of detailed balance. This paper will be denoted as SDS III. The existence of a dynamical potential with both local and global meanings in general…
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…
Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly…