Related papers: Renewal and Regenerative Processes: short review
In the continuity of a recent paper ([6]), dealing with finite Markov chains, this paper proposes and analyzes a recursive algorithm for the approximation of the quasi-stationary distribution of a general Markov chain living on a compact…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
We consider the almost semi-continuous processes defined on a finite Markov chain. The representation of the moment generating functions for the absolute maximum after achievement positive level and for the recovery time are obtained.…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
Martingales constitute a basic tool in stochastic analysis; this paper considers their application to counting processes. We use this tool to revisit a renewal theorem and its extensions for various counting processes. We first consider a…
We investigate the concatenation of Markov processes. Our primary concern is to utilize processes constructed in this manner for Monte Carlo integration. To enable this using conventional methods, it is essential to demonstrate the Markov…
The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a…
Despite the numerous applications that may be expeditiously modelled by counting processes, stochastic filtering strategies involving Poisson-type observations still remain somewhat poorly developed. In this work, we propose a Monte Carlo…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
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…
This chapter presents an introduction to Markovian modeling for the analysis of sequence data. Contrary to the deterministic approach seen in the previous sequence analysis chapters, Markovian models are probabilistic models, focusing on…
We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying $\Phi f \geq 0$ for some linear operator $\Phi$. We introduce a new…
Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…
This initial version of this document was written back in 2014 for the sole purpose of providing fundamentals of reliability theory as well as to identify the theoretical types of machinery for the prediction of durability/availability of…
We study the loop clusters induced by Poissonian ensembles of Markov loops on a finite or countable graph (Markov loops can be viewed as excursions of Markov chains with a random starting point, up to re-rooting). Poissonian ensembles are…
Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…
We study the connections existing between max-infinitely divisible distributions and Poisson processes from the point of view of functional analysis. More precisely, we derive functional identities for the former by using well-known results…
We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an…
In this paper we study various properties of finite stochastic systems or hidden Markov chains as they are alternatively called. We discuss their construction following different approaches and we also derive recursive filtering formulas…