Related papers: Hitting Times for Continuous-Time Imprecise-Markov…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
The main subject of the study in this paper is the simultaneous renewal time for two time-inhomogeneous Markov chains which start with arbitrary initial distributions. By a simultaneous renewal we mean the first time of joint hitting the…
In this paper, we are interested in investigating the perturbation bounds for the stationary distributions for discrete-time or continuous-time Markov chains on a countable state space. For discrete-time Markov chains, two new norm-wise…
Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered:…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
The paper studies an improved estimate for the rate of convergence for nonlinear homogeneous discrete-time Markov chains. These processes are nonlinear in terms of the distribution law. Hence, the transition kernels are dependent on the…
We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$…
We establish general theorems quantifying the notion of recurrence --- through an estimation of the moments of passage times --- for irreducible continuous-time Markov chains on countably infinite state spaces. Sharp conditions of…
When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This is done by considering as basic uncertainty models the so-called credal sets that…
We generalize the notion of strong stationary time and we give a representation formula for the hitting time to a target set in the general case of non-reversible Markov processes.
We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…
We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…
We develop some sufficient conditions for the stochastic ordering between hitting times, in a fixed state, for two Markov chains. In particular, we focus attention on the so called \emph{skip-free} case. In the analysis of such a case, we…
Stochastic time-varying optimization is an integral part of learning in which the shape of the function changes over time in a non-deterministic manner. This paper considers multiple models of stochastic time variation and analyzes the…
This paper focuses on a class of continuous-time controlled Markov chains with time-inconsistent and distribution-dependent cost functional (in some appropriate sense). A new definition of time-inconsistent distribution-dependent…
In the absence of acceleration, the velocity formula gives "distance travelled equals speed multiplied by time". For a broad class of Markov chains such as circulant Markov chains or random walk on complete graphs, we prove a probabilistic…
The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer…