Related papers: Random time-changes and asymptotic results for a c…
In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We consider continuous-time Markov chain on a finite state space X. We assume X can be clustered into several subsets such that the intra-transition rates within these subsets are of order $\mathcal{O}(\frac{1}{\epsilon})$ comparing to the…
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov…
In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is…
In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…
We consider continuous-space, discrete-time Markov chains on $\mathbb{R}^d$, that admit a finite number $N$ of metastable states. Our main motivation for investigating these processes is to analyse random Poincar\'e maps, which describe…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…