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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: "Identifying similar birth-death processes using chain sequences. "

Presented by "Erik van Doorn, Department of Mathematical Sciences, University of Twente, The Netherlands ",

21 August 2000 00:00 in CM221

"The model we consider is that of a birth-death process X = {X(t)} taking values in N = {0,1,...}. To envisage such a process it is convenient to think of a particle travelling through the state space N in such a way that it stays in each state during an exponentially distributed amount of time (with state-dependent mean), after which it jumps to one of the neighbouring states with certain (state-dependent) probabilities. The stochastic variable X(t) can then be interpreted as the state of the particle at time t. We allow the probability of a downward jump in tate 0 to be positive, so that escape from N is possible. Two birth-death processes are called similar if the ratio of their transition probabilities is independent of time. We will show which condition the parameters of a birth-death process should satisfy in order that the process belongs to a (one-parameter) family of similar processes, and we will identify the members of such a family. An important ingredient in solving these problems is the use of chain sequences. The talk is based on joint work with R.B. Lenin, P.R. Parthasarathy and W.R.W. Scheinhardt. "

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