Related papers: A martingale approach for P\'olya urn processes

This work is a continuation of [7]. We consider a continuous-time birth-and-death process in which the transition rates have an asymptotical power-law dependence upon the position of the process. We establish rough exponential asymptotic…

In this paper, we investigate the parameter estimation problem for reflected OU processes. Both the estimates based on continuously observed processes and discretely observed processes are considered. The explicit formulas for the…

We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a…

The Bernoulli-Laplace model describes a diffusion process of two types of particles between two urns. To analyze the finite-size dynamics of this process, and for other constructive results we diagonalize the corresponding transition matrix…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood…

The slow processes of metastable stochastic dynamical systems are difficult to access by direct numerical simulation due the sampling problem. Here, we suggest an approach for modeling the slow parts of Markov processes by approximating the…

We propose a method of detecting a phase transition in a generalized P\'olya urn in an information cascade experiment. The method is based on the asymptotic behavior of the correlation $C(t)$ between the first subject's choice and the…

In this paper, we propose a general mathematical framework to represent many multi-agent signalling systems in recent works. Our goal is to apply previous results in monotonicity to this class of systems and study their asymptotic behavior.…

This paper revisits the problem of estimating the fractional Ornstein - Uhlenbeck process observed in a linear channel with white noise of small intensity. We drive the exact asymptotic formulas for the mean square errors of the filtering…

We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting…

A stationary Poisson line tessellation is considered whose directional distribution is concentrated on two different atoms with some positive weights. The shape of the typical cell of such a tessellation is studied when its area or its…

Knowing how and when trends are formed is a frequently visited research goal. In our work, we focus on the progression of trends through (social) networks. We use a random graph (RG) model to mimic the progression of a trend through the…

We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of…

We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…

We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past…

Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…

Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent…

The fringe of a B-tree with parameter $m$ is considered as a particular P\'olya urn with $m$ colors. More precisely, the asymptotic behaviour of this fringe, when the number of stored keys tends to infinity, is studied through the…

This survey is an introduction to asymptotic methods for portfolio-choice problems with small transaction costs. We outline how to derive the corresponding dynamic programming equations and simplify them in the small-cost limit. This allows…