A recursion theorem on solving differential-difference equations and applications to some stochastic processes

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Abstract
Summary A recursive procedure leading to the solution of triangular systems of differential-difference equations is presented. It is shown that the equations for special families of multi-dimensional pure birth processes and pure death processes can be represented as such a system. The theory is used to resolve a difficult problem of stochastic cross-infection among groups. Additional applications to problems in epidemic theory are discussed.