Related papers: Moment properties for two-type continuous-state br…
A version of the second order phase transition theory, in which the Nernst theorem holds automatically, is proposed. The theory is constructed in terms of the order parameter and the (configurational) entropy. It faithfully reproduces the…
We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing one. In particular, we may start with a superprocess,…
We give an analytic proof of the asymptotic behaviour of the moments of moments of the characteristic polynomials of random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for the leading order…
The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…
We explore the behavior and establish new properties of the cumulative-sum process (CUSUM) and its running maximum. The study includes precise expressions for CUSUM's moment generating function and moments, fast recursive computing…
We introduce polynomial processes taking values in an arbitrary Banach space $B$ via their infinitesimal generator $L$ and the associated martingale problem. We obtain two representations of the (conditional) moments in terms of solutions…
We obtain quantitative Four Moments Theorems establishing convergence of the laws of elements of a Markov chaos to a Pearson distribution, where the only assumption we make on the Pearson distribution is that it admits four moments. While…
This article study the average conditioning for a random underdetermined polynomial system. The expected value of the moments of the condition number are compared to the moments of the condition number of random matrices. An expression for…
Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a L\'evy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In…
Motivated by applications to COVID dynamics, we describe a branching process in random environments model $\{Z_n\}$ whose characteristics change when crossing upper and lower thresholds. This introduces a cyclical path behavior involving…
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic…
In this paper we consider a ring of $N\ge 1$ queues served by a single server in a cyclic order. After having served a queue (according to a service discipline that may vary from queue to queue), there is a switch-over period and then the…
The non-equilibrium steady states emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution…
Consider a finite renewal process in the sense that interrenewal times are positive i.i.d. variables and the total number of renewals is a random variable, independent of interrenewal times. A finite point process can be obtained by…
We give a new framework for proving the existence of low-degree, polynomial approximators for Boolean functions with respect to broad classes of non-product distributions. Our proofs use techniques related to the classical moment problem…
We study a class of stationary Markov processes with marginal distributions identifiable by moments such that every conditional moment of degree say $m$ is a polynomial of degree at most $m\;\text{.}\;$ We show that then under some…
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…
This paper is a complement to the studies on the minimum of a real-valued branching random walk. In the boundary case (Biggins, Kyprianou 2005), A\"{i}d\'ekon in a seminal paper (2013) obtained the convergence in law of the minimum after a…