Advances in Applied Probability

Motivated by recent studies of big samples, this work aims to construct a parametric model which is characterized by the following features: (i) a ‘local’ reinforcement, i.e. a reinforcement mechanism mainly based on the last observations, (ii) a rando…

We use probabilistic methods to study properties of mean-field models, which arise as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that n particles move forward on the real line. S…

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of the order

for the nth i…

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of the order

for the nth i…

We consider a sequence of Poisson cluster point processes on

: at step

of the construction, the cluster centers have intensity

for some

, and each cluster consists of the particles of a branching random walk up to generation n—g…

We consider a sequence of Poisson cluster point processes on

: at step

of the construction, the cluster centers have intensity

for some

, and each cluster consists of the particles of a branching random walk up to generation n—g…

This paper provides a full classification of the dynamics for continuous-time Markov chains (CTMCs) on the nonnegative integers with polynomial transition rate functions and without arbitrary large backward jumps. Such stochastic processes are abunda…