Related papers: On exponential recurrence of "Markov-up'' processe…
A hidden Markov process is a well known concept in information theory and is used for a vast range of applications such as speech recognition and error correction. We bridge between two disciplines, experimental physics and advanced…
Let $f$ be the density function associated to a matrix-exponential distribution of parameters $(\alpha, T,s)$. By exponentially tilting $f$, we find a probabilistic interpretation which generalises the one associated to phase-type…
We provide a criterion for establishing lower bounds on the rate of convergence in $f$-variation of a continuous-time ergodic Markov process to its invariant measure. The criterion consists of novel super- and submartingale conditions for…
Markov-modulated L\'evy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modulation, accompanied by jumps. We give explicit expressions…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
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…
In this paper it is shown that adaptive importance sampling algorithms converge at exponential rate for Markov chain expectation problems that admit a combination of a filtered estimator and a Markov zero-variance measure. It extends a…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
In this article, we introduce \textit{Mallows processes}, defined to be continuous-time c\`adl\`ag processes with Mallows distributed marginals. We show that such processes exist and that they can be restricted to have certain natural…
We study a Markov process with two components: the first component evolves according to one of finitely many underlying Markovian dynamics, with a choice of dynamics that changes at the jump times of the second component. The second…
We construct the non-linear Markov process connected with biological model of bacterial genome recombination. The description of invariant measures of this process gives us the solution of one problem in elementary probability theory.
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…
Processes having the same bridges as a given reference Markov process constitute its {\it reciprocal class}. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set $\mathcal{A} \subset…
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-reinforced random walks is significantly growing in recent years as they are much better at modeling high dimensional data and nonlinear dynamics in…
In the theory of testing for Markovian processes developed so far, exponentially timed internal actions are not admitted within processes. When present, these actions cannot be abstracted away, because their execution takes a nonzero amount…
Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…
Reinforcement Learning Algorithms are predominantly developed for stationary environments, and the limited literature that considers nonstationary environments often involves specific assumptions about changes that can occur in transition…