a r t i c l e i n f o a b s t r a c t MSC: 34D20 34K50 60H10 93E15 Keywords: Pure delay system Two-timescale Markov chain Stationary distribution Almost sure uniform stability Yorke's condition This work examines almost sure stability of a pure random delay system whose delay time is modeled by a finite state continuous-time Markov chain with two-time scales. The Markov chain contains a fast-va...

We introduce the concepts of lumpability and commutativity of a continuous time discrete state space Markov process, and provide a necessary and sufficient condition for a lumpable Markov process to be commutative. Under suitable conditions we recover some of the basic quantities of the original Markov process from the jump chain of the lumped Markov process.

Hidden Markov models have proved to be a very exible class of models, with many and diverse applications. Recently Markov chain Monte Carlo (MCMC) techniques have provided powerful computational tools to make inferences about the parameters of hidden Markov models, and about the unobserved Markov chain, when the chain is deened in discrete time. We present a general algorithm, based on reversib...

Jump Markov linear systems are linear systems whose parameters evolve with time according to a finite-state Markov chain. Given a set of observations, our aim is to estimate the states of the finite-state Markov chain and the continuous (in space) states of the linear system. The computational cost in computing conditional mean or maximum a posteriori (MAP) state estimates of the Markov chain o...

The aim of this thesis is to investigate the mathematics of Markov-modulated models for derivatives pricing. We consider a model where instantaneous stock volatility and drift are driven by a continuous time finite Markov chain. We present a new derivation of an integral representation for attainable non-path dependent options’ prices in a twostate and three-state Markov chain model, and comput...

abstract agricultural scientists have developed considerable interest in modeling and generation of rainfall as new ways of analyzing rainfall data and assessing its impact on agriculture. a combination of markov chain and gamma distribution function is recognized as a simple approach and is demonstrated to be effective in generating daily rainfall data for many environments. thus the availabil...

Motivated by an original on-line page-ranking algorithm, starting from an arbitrary Markov chain (Cn) on a discrete state space S, a Markov chain (Cn, Mn) on the product space S, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both coordinates are equal. The asymptotic pro...

The paper attempts to provide forecast methodological framework and concrete models to estimate long run probability of default term structure for Hungarian corporate debt instruments, in line with IFRS 9 requirements. Long run probability of default and expected loss can be estimated by various methods and has fifty-five years of history in literature. After studying literature and empirical m...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

This paper is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. The consensus control is achieved by using stochastic approximation methods. In the setup, the regime-switching process (the Markov chain) contains a rate paramet...