This paper investigates optimal portfolio strategies in a market where the drift is driven by an unobserved Markov chain. Information on the state of this chain is obtained from stock prices and expert opinions in the form of signals at random discrete time points. As in Frey et al. (2012), Int. J. Theor. Appl. Finance, 15, No. 1, we use stochastic filtering to transform the original problem in...

We consider a discrete-time Markov chain on the non-negative integers with drift to innnity and study the limiting behaviour of the state probabilities conditioned on not having left state 0 for the last time. Using a transformation, we obtain a dual Markov chain with an absorbing state such that absorption occurs with probability 1. We prove that the state probabilities of the original chain c...

The theory of general state-space Markov chains can be strongly related to the case of discrete state-space by use of the notion of small sets and associated minorization conditions. The general theory shows that small sets exist for all Markov chains on state-spaces with countably generated σ-algebras, though the minorization provided by the theory concerns small sets of order n and n-step tra...

The theory of general state-space Markov chains can be related strongly to the case of discrete state-space by use of Doeblin’s notion of small sets and associated minorization conditions. The general theory shows that small sets exist for all Markov chains on state-spaces with countably generated -algebras, though the minorization provided by the theory concerns n-step transition kernels for s...

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...

Wireless channels usually face bursty errors, i.e., errors are prone to occur in clusters. These bit errors can be modeled using the Gilbert-Elliott model. When data packets are transferred over channels with bursty errors, packet error statistics are more important than bit error statistics to analyze the communication performance. This has been modeled as a discrete time Markov chain (DTMC) i...

A bivariate Markov process comprises a pair of random processes which are jointly Markov. One of the two processes in that pair is observable while the other plays the role of an underlying process. We are interested in three classes of bivariate Markov processes. In the first and major class of interest, the underlying and observable processes are continuous-time with finite alphabet; in the s...

A wide variety of problems in the domain of directed percolation theory, contact process, voter models rely on the analysis of a infinite absorbing Markov chain. Although results for these problems have been obtained through other approaches, reasoning about the Markov chain gives rise to elegant results that are often explicit functions of the chain parameters. This allows results to be reused...

We develop the statistical theory of discrete nonstationary non-Markov random processes in complex systems. The objective of this paper is to find the chain of finite-difference non-Markov kinetic equations for time correlation functions (TCF) in terms of nonstationary effects. The developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of ini...