the notion of infinite order markov process is introduced and the markov property of the flow of information is established.

Abstract. In this research we try to consider the problem of applying the Nonhomogeneous Poisson process to trends of economic development. More specifically, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean and the variance of the modified process ...

In this paper, we establish a relation between growing networks and Markov chains, and propose a computational approach for network degree distributions. Using the Barabási-Albert model as an example, we first show that the degree evolution of a node in a growing network follows a nonhomogeneous Markov chain. Exploring the special structure of these Markov chains, we develop an efficient algori...

Markov switching models can be used to study heterogeneous populations that are observed over time. This paper explores modeling the group characteristics nonparametrically, under both homogeneous and nonhomogeneous Markov switching for group probabilities. The model formulation involves a finite mixture of conditionally independent Dirichlet process mixtures, with a Markov chain defining the m...

This report addresses the broad role of aftershocks in the Performance-based Earthquake Engineering (PBEE) process. This is an area which has, to date, not received careful scrutiny nor explicit quantitative analysis. We begin by introducing Aftershock Probabilistic Seismic Hazard Analysis (APSHA). APSHA, similar to conventional mainshock PSHA, is a procedure to characterize the timevarying aft...

This paper deals with aspects of the limit behaviour of products of nonidentical finite or countable stochastic matrices (P). Applications n are given to nonhomogeneous Markov models as positive chains, some classes of finite chains considered by Doeblin and weakly ergodic chains.