Related papers: Monotonicity and complete monotonicity for continu…
In the paper we study continuous time controlled Markov processes using discrete time controlled Markov processes. We consider long run functionals: average reward per unit time or long run risk sensitive functional. We also investigate…
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
During the past 15 years, several extensions of the concepts noise sensitivity and noise stability, first coined in~\cite{schramm2000}, has been studied. The purpose in this paper is to give definitions of this concepts in the setting of…
In this paper we study the additive functionals of Markov chains via conditioning with respect to both past and future of the chain. We shall point out new sufficient projective conditions, which assure that the variance of partial sums of…
The paper is largely of a review nature. It considers two main methods used to study stability and obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable…
We introduce and analyze a new class of monotone stochastic recursions in a regenerative environment which is essentially broader than that of Markov chains. We prove stability theorems and apply our results {to three canonical models in…
Two types of dynamics, chaotic and monotone, are compared. It is shown that monotone maps in strongly ordered spaces do not have chaotic attracting sets.
We investigate the mixing properties of a finite Markov chain in random environment defined as a mixture of a deterministic chain and a chain whose state space has been permuted uniformly at random. This work is the counterpart of a…
We consider prediction theory for stationary stochastic processes in continuous time. We discuss prediction using the whole (infinite) past, and using only a finite section of the past. The solutions to both these classical problems have…
In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains (CTMCs). The equilibrium / transient behaviour of such…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…
We consider $k$-dimensional discrete-time systems of the form $x_{n+1}=F(x_n,\ldots,x_{n-k+1})$ in which the map $F$ is continuous and monotonic in each one of its arguments. We define a partial order on $\mathbb{R}^{2k}_+$, compatible with…
Let $(X_t)_{t = 0 }^{\infty}$ be an irreducible reversible discrete time Markov chain on a finite state space $\Omega $. Denote its transition matrix by $P$. To avoid periodicity issues (and thus ensuring convergence to equilibrium) one…
In this paper, we consider two time-inhomogeneous Markov chains $X^{(l)}_t$, $l\in\{1,2\}$, with discrete time on a general state space. We assume the existence of some renewal set $C$ and investigate the time of simultaneous renewal, that…
We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of…
In this paper we develop the elements of the theory of algorithmic randomness in continuous-time Markov chains (CTMCs). Our main contribution is a rigorous, useful notion of what it means for an individual trajectory of a CTMC to be random.…
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows…
We establish that a mode-coupling approximation for the dynamics of multi-component systems obeying Smoluchowski dynamics preserves a subtle yet fundamental property: the matrices of partial density correlation functions are completely…
We are interested in quasi-stationarity and quasi-ergodicity when the absorbing boundary is moving. First we show that, in the moving boundary case, the quasi-stationary distribution and the quasi-limiting distribution are not well-defined…
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…