Related papers: A solvable class of renewal processes
We establish the general equivalence between rare event process for arbitrary continuous functions whose maximal values are achieved on non-trivial sets, and the entry times distribution for arbitrary measure zero sets. We then use it to…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…
We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and infinite measure semiflows. Examples of systems covered by our results include suspensions over…
We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…
In this note, we consider the problem of robust learning mixtures of linear regressions. We connect mixtures of linear regressions and mixtures of Gaussians with a simple thresholding, so that a quasi-polynomial time algorithm can be…
We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…
The scaling properties of the roughness of surfaces grown by two different processes randomly alternating in time, are addressed. The duration of each application of the two primary processes is assumed to be independently drawn from given…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…
We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local…
We introduce and study renewal processes defined by means of extensions of the standard relaxation equation through ``stretched" non-local operators (of order $\alpha$ and with parameter $\gamma$). In a first case we obtain a generalization…
In this paper, we study the existence and uniqueness of solutions for general fractional-time parabolic equations of mixture type, and their probabilistic representations in terms of the corresponding inverse subordinators with or without…
In this note we explain two transitions known for moment generating functions of local times by means of properties of the renewal measure of a related renewal equation. The arguments simplify and strengthen results on the asymptotic…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…
It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.l.l.) solutions enables one to construct the associated transition probability functions. We extend this result to the case when the martingale…
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…