## Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients.(English)Zbl 0959.60048

It is considered a system of linear hyperbolic equations describing a simple transport model in which particles of type $$p$$ change to particles of type $$q$$ and conversely. The associated initial-boundary value problem of this deterministic system is reconsidered probabilistically involving a homogeneous stochastic process which evolves accordingly to the given partial differential equations. The approximate solution of the simple transport model is connected with a heat equation and its deviation from the exact solution is analyzed via central limit theorem and large deviation estimates. There are given and proved two theorems.

### MSC:

 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35L99 Hyperbolic equations and hyperbolic systems 60F05 Central limit and other weak theorems 60G99 Stochastic processes 65C30 Numerical solutions to stochastic differential and integral equations 92C20 Neural biology
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