Given a Markov process with state space {0, 1} we treat parameter estimation of the transition intensities and state estimation of unobserved portions of the sample path, based on various partial observations of the process. Parameter estimators are devised and shown to be consistent and...

Let M be a Poisson random measure on [0, [infinity]) and let {X(t): t[epsilon][0,[infinity])} be an alternating renewal process induced by the probability measures [eta] and [mu];i.e., X alternates between the states 1 and 0 with independent sojourns, those in 1 having distribution [eta] and...

Let (E, ) be a measurable space and let [eta] be a probability measure on . Denote by I([eta]) the set of Markov kernels P over (E, ) for which [eta] is an invariant measure: [eta] = [eta]P. We characterize the extreme points of I([eta]) in this paper. When E is a finite set, I([eta]) is a...

Let N be an observable Cox process on a locally compact space E directed by an unobservable random measure M. Techniques are presented for estimation of M, using the observations of N to calculate conditional expectations of the form E [M]A], where A is the [sigma]-algebra generated by the...

Let Ni, i[greater-or-equal, slanted]1, be i.i.d. observable Cox processes on a compact metric space E, directed by unobservable random measures Mi. Assume that the probability law of the Mi is completely unknown. Techniques are developed for approximation of state estimators using data from the...