Stochastic track structure models

In contrast to liquid water, a detailed mechanistic understanding of the physical and chemical processes occurring in the evolution of the radiation chemical track in hydrocarbons is not available except on the most empirical level. Stochastic diffusion-kinetic calculations for low permittivity media have been limited to simple studies of cation-electron recombination in aliphatic hydrocarbons employing idealized track structures [56-58], and simplistic deterministic calculations have been used to model the radical and excited state chemistry [102]. While these calculations have been able to reproduce measured free ion yields and end product yields, respectively, the lack of a detailed mechanistic model makes it very difficult... 

Besides the hypothesis of spatially homogeneous processes in this stochastic formulation, the particle model introduces a structural heterogeneity in the media through the scarcity of particles when their number is low. In fact, the number of differential equations in the stochastic formulation for the state probability keeps track of all of the particles in the system, and therefore it accounts for the particle scarcity. The presence of several differential equations in the stochastic formulation is at the origin of the uncertainty, or stochastic error, in the process. The deterministic version of the model is unable to deal with the stochastic error, but as stated in Section 9.3.4, that is reduced to zero when the number of particles is very large. Only in this last case can the set of Kolmogorov differential equations be adequately approximated by the deterministic formulation, involving a set of differential equations of fixed size for the states of the process. 

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