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2 results

A Limit Theorem for a Weiss Epidemic Process
Part of
A. V. Kalinkin, A. V. Mastikhin
Journal:

Journal of Applied Probability / Volume 52 / Issue 1 / March 2015

Published online by Cambridge University Press:

30 January 2018, pp. 247-257

Print publication:

March 2015
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For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.

The branching property in generalized information theory
Bruce Ebanks
Journal:

Advances in Applied Probability / Volume 10 / Issue 4 / December 1978

Published online by Cambridge University Press:

01 July 2016, pp. 788-802

Print publication:

December 1978
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It is shown that every measure of expected information which has the branching property is of the form where J is a given information measure which is compositive under a regular binary operation and the Ψn are antisymmetric, bi-additive functions. In a probability space, such measures (entropies) take the form