This paper contains the proof of the positivity of the top Lyapunov exponent for the multiplicative stochastic integrals related to the diffusion processes on the Lee algebra of the matrices with zero trace.

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Work is performed within a cascade and probabilistic method which essence consists in receiving and further usage of the cascade and probabilistic functions (CPF) for various particles. CPF make sense to probability that the particle generated at some depth of h' will reach a certain depth of h after n number of impacts. In work optimization calculation algorithms of the cascade and probabilistic functions (CPF) depending on interactions number and particles penetration depth is offered, concentration of radiation defects at ionic radiation for the purpose of reduction calculation time and quality. For calculation CPF and concentration radiation defects there is an area of result, border of this area and a calculation step. Borders and a calculation step selection automation is executed.