In this paper, we study the problems of sequential probability ratio tests for parameterized
hidden Markov models. We investigate in some detail the performance of the tests and derive …

Let ξ 0 ,ξ 1 ,…,ξ ω−1 be observations from the hidden Markov model with probability
distribution P θ 0 , and let ξ ω ,ξ ω+1 ,… be observations from the hidden Markov model with …

In the 1960s, Shiryaev developed a Bayesian theory of change-point detection in the iid case,
which was generalized in the early 2000s by Tartakovsky and Veeravalli and recently by …

In this paper, the quickest change detection problem is studied in two-state hidden Markov
models (HMM), where the vector parameter θ of the HMM changes from θ 0 to θ 1 at some …

In this article, we consider a model of time-varying volatility which generalizes the classical
Black-Scholes model to include regime-switching properties. Specifically, the unobservable …

Let X be an irreducible, aperiodic and positive recurrent Markov chain with a countably infinite
state space S and transition probability matrix P. Let π be the stationary probability and T k …

We prove a d-dimensional renewal theorem, with an estimate on the rate of convergence, for
Markov random walks. This result is applied to a variety of boundary crossing problems for …

To minimize the variance of Monte Carlo estimators, we develop a novel exponential
embedding technique that extends the classical concept of sufficient statistics in importance …

Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in
stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state …

Degradation analysis is a tool for assessing the lifetime distribution in reliability analysis.
The lifetime of a product, in degradation analysis, is defined as the time when the value of a …