Related papers: Regenerative processes
We prove several forms of renewal theorem tailored to renewal processes with marks and clusters. In particular, for an i.i.d. sequence $(\xi_i,X_i)_{i \geq 0}$, where $\xi_0$ denotes a finite point process on $\mathbb{R}$ and $X_0$ denotes…
We introduce a single generative mechanism with which it is able to describe diverse non-stationary diffusions. A non-stationary Markovian replication process for steps is considered, for which we analytically derive time-evolution of the…
Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
Linear fractional Galton-Watson branching processes in i.i.d.~random environment are, on the quenched level, intimately connected to random difference equations by the evolution of the random parameters of their linear fractional marginals.…
Retrial phenomenon naturally arises in various systems such as call centers, cellular networks and random access protocols in local area networks. This paper gives a comprehensive survey on theory and applications of retrial queues in these…
We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy…
We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…
Given a two-sided real-valued L\'evy process $(X_t)_{t \in \mathbb{R}}$, define processes $(L_t)_{t \in \mathbb{R}}$ and $(M_t)_{t \in \mathbb{R}}$ by $L_t := \sup\{h \in \mathbb{R} : h - \alpha(t-s) \le X_s \text{ for all } s \le t\} =…
Distributed storage systems provide large-scale reliable data storage services by spreading redundancy across a large group of storage nodes. In such a large system, node failures take place on a regular basis. When a storage node breaks…
This paper analyzes stochastic networks consisting of finite capacity nodes with different classes of requests which move according to some routing policy. The Markov processes describing these networks do not, in general, have…
We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on…
This paper introduces a unified theoretical perspective that views deep generative models as probability transformation functions. Despite the apparent differences in architecture and training methodologies among various types of generative…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
Power systems are subject to fundamental changes due to the increasing infeed of renewable energy sources. Taking the accompanying decentralization of power generation into account, the concept of prosumer-based microgrids gives the…
We study a renewal problem within a periodic environment, departing from the classical renewal theory by relaxing the assumption of independent and identically distributed inter-arrival times. Instead, the conditional distribution of the…
We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…
This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…
Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…
We study a self-consistent approach to introduce higher-order effects in a branching process model of complex contagion on clustered networks. Branching processes operate over an infinite population such that they never circle back and…