No abstract

"A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process."

No abstract

In a previous investigation (Torrez (1978)) conditions were given for extinction and instability of a stochastic process (Zn ) evolving in a random environment controlled by an irreducible Markov chain (Yn ) with state space 𝒴 The process (Yn, Zn ) is Markovian with state space 𝒴 × {0,1, ···, N} where 𝒴 = {1,· ··,m} and the marginal process (Zn ) is a birth and death chain on {0,1,· ··,N}, with 0 and N made absorbing, when conditioned on a fixed sequence of environmental states of (Yn ). This paper provides bivariate finite difference methods for calculating (i) P(Zn → 0) when this probability is not one; and (ii) the expected duration of the process Zn. For (i), the cases when the transition probabilities of the (Yn )-conditioned process (Zn ) are non-homogeneous and homogeneous are considered separately. Examples are given to illustrate these methods.

Redundant data from independent over-thehorizon radar systems can increase track accuracy by providing more independent "looks" at the target. With proper geometry, complementary radar system can aid in resolving uncertainties in the coordinate registration through the various ionospheric modes. Systematic positional differences between tracks from the separate radars can be used to improve the estimation of ionospheric heights. In operational systems, targets are tracked by multiple over-thehorizon radars in overlapping coverage areas. In this paper, we consider the case of two over-the-horizon radars. The main algorithm is designed to hand-off range bias errors from one radar's ionospheric mode to a second radar. It is expected that the resultant algorithmic development based on the work described in this paper will improve track positional accuracy by more than 50%.