Probabilistic Methods in Applied Mathematics e-bog

Probabilistic Methods in Applied Mathematics, Volume 3 focuses on the influence of the probability theory on the formulation of mathematical models and development of theories in many applied fields. The selection first offers information on statistically well-set Cauchy problems and wave propagation in random anisotropic media. Discussions focus on extension to biaxial anisotropic random media; an effective medium description for a random uniaxial anisotropic medium and the resulting dyadic Green's function; evolution of the spectral matrix measure; and well-set Cauchy problems. The text then examines stochastic processes in heat and mass transport, including mass transport, velocity field, temperature transport, and coupling of mass and heat transport. The manuscript takes a look at the potential theory for Markov chains and stochastic differential games. Topics include formal solutions for some classes of stochastic linear pursuit-evasion games; solution of a stochastic linear pursuit-evasion game with nonrandom controls; problems of potential theory; and hitting distributions. The selection is a vital source of data for mathematicians and researchers interested in the probability theory.