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An exponential hidden Markov model (EHMM) is a hidden Markov model which consists of a pair of stochastic processes {Xt, Yt}t∈N .{Yt}t∈N is influenced by {Xt}t∈N , which is assumed to form a Markov chain. {Xt}t∈N is not observed. {Yt}t∈N is an observation process and Yt given Xt has exponential distribution. In this paper, we estimate the parameter of EHMM and study the convergence of the parameter estimator sequence. EHMM is characterized by a parameter φ = (A,λ) where A is a transition matrix of Xt and λ is a vector of parameters of probability density function of Yt given Xt. To determine the parameter estimator, a maximum likelihood method is used. Numerical approximation is used through an Expectation Maximization (EM) algorithm. Under the continuous assumption, the sequence {φ(k)} obtained by the EM algorithm, converges to φ which is the stationary point of ln Lt(φ) and the sequence {lnLt(φ (k))} increasingly converges to ln Lt(φ ). AMS Subject Classification: 30B30, 62L12

PARAMETER ESTIMATION OF EXPONENTIAL HIDDEN MARKOV MODEL AND CONVERGENCE OF ITS PARAMETER ESTIMATOR SEQUENCE