Related papers: A martingale approach for P\'olya urn processes
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
In this paper we generalize the martingale of Kella and Whitt to the setting of L\'{e}vy-type processes and show that the (local) martingales obtained are in fact square integrable martingales which upon dividing by the time index converge…
This paper extends the link between stochastic approximation (SA) theory and randomized urn models developed in Laruelle, Pag{\`e}s (2013), and their applications to clinical trials introduced in Bai, HU (1999,2005) and Bai, Hu, Shen…
Microscopic thermal machines that are of the dimensions of around few hundred nanometers have been the subject of intense study over the last two decades. Recently, it has been shown that the efficiency of such thermal engines can be…
We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form $\frac{1}{Z_n} \big|\det \big( M^2-tI \big)\big|^{\alpha} e^{-n\operatorname{Tr} V(M)}dM$, where $M$ is an $n\times…
Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times scales of widely differing orders of magnitude. By the law of mass action, the process is…
We study the asymptotic behavior of the expectation of the maxima and minima of random assignment process generated by a large matrix with multinomial entries. A variety of results is obtained for different sparsity regimes.
In this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after $T$, of a Volterra process driven by a…
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure…
The Fleming-Viot process with parent-independent mutation process is one particular neutral population genetic model. As time goes by, some initial species are replaced by mutated ones gradually. Once the population mutation rate is high,…
We investigate the randomized Karlin model with parameter $\beta\in(0,1)$, which is based on an infinite urn scheme. It has been shown before that when the randomization is bounded, the so-called odd-occupancy process scales to a fractional…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
We consider a stochastic process in which independent identically distributed random matrices are multiplied and where the Lyapunov exponent of the product is positive. We continue multiplying the random matrices as long as the norm,…
This article examines large time behaviour of finite state mean-field interacting particle systems. Our first main result is a sharp estimate (in the exponential scale) on the time required for convergence of the empirical measure process…
Conditions are given under which the empirical copula process associated with a random sample from a bivariate continuous distribution has a smaller asymptotic covariance function than the standard empirical process based on observations…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
Neural networks are becoming an increasingly important tool in applications. However, neural networks are not widely used in statistical genetics. In this paper, we propose a new neural networks method called expectile neural networks. When…
We obtain the strong asymptotics of polynomials $p_n(\lambda)$, $\lambda\in\mathbb{C}$, orthogonal with respect to measures in the complex plane of the form $$ e^{-N(|\lambda|^{2s}-t\lambda^s-\overline{t\lambda}^s)}dA(\lambda), $$ where $s$…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…