Related papers: Comparison of Markov processes by the martingale c…
Using backward propagators, we construct inhomogeneous Random Evolutions on Banach spaces driven by (uniformly ergodic) Semi-Markov processes. After studying some of their properties (measurability, continuity, integral representation), we…
McCullagh and Yang (2006) suggest a family of classification algorithms based on Cox processes. We further investigate the log Gaussian variant which has a number of appealing properties. Conditioned on the covariates, the distribution over…
Big networks express various large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big…
This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying…
We develop a martingale approximation approach to studying the limiting behavior of quadratic forms of Markov chains. We use the technique to examine the asymptotic behavior of lag-window estimators in time series and we apply the results…
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…
Herein, the Hidden Markov Model is expanded to allow for Markov chain observations. In particular, the observations are assumed to be a Markov chain whose one step transition probabilities depend upon the hidden Markov chain. An…
In this paper we introduce a variant of Burkholder's martingale transform associated with two martingales with respect to different filtrations. Even though the classical martingale techniques cannot be applied, we show that the discussed…
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…
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.
This paper shows how one can use Sequential Monte Carlo methods to perform what is typically done using Markov chain Monte Carlo methods. This leads to a general class of principled integration and genetic type optimization methods based on…
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra…
The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description…
We examine the effect of item arrangement on choices using a novel decision-making model based on the Markovian exploration of choice sets. This model is inspired by experimental evidence suggesting that the decision-making process involves…
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…