Stochastic Model for Bimolecular Reaction

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Abstract
The kinetics of two bimolecular reactions A+B→C and 2A→C are investigated by the theory of stochastic process, in which the number of molecules of reactive substances is a discrete random variable. The set of fundamental differential‐difference equations satisfying the probability distribution for the number of reactive molecules is solved by the method of Laplace transformation. The mathematical expectation and variance are derived from the generating functions, which can be expressed by Jacobi's polynomial for A+B→C and by Legendre's polynomial for 2A→C. The stochastic models are discussed in comparison with the deterministic models, and it is proved that the stochastic rate equations are not consistent with the deterministic rate equations in the mean.

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