文档介绍：Stochastic Models and Monte Carlo Methods in
Numerical Mathematics and Mathematical
Physics
Abstract.
Stochastic models serve nowadays as a powerful instrument for studying
the dynamics of processes in natural and life sciences, in the broad spec-
trum, from simple models of financial mathematics in the form of systems of
stochastic differential equations, to plicated turbulence models in-
volving PDE’s whose parameters are random fields, governing the movement
of energy spectrum from smallest viscous scales to large energy-containing
vorteces in the boundary-layer of atmosphere. The principal research efforts
are directed to the development of new stochastic models and simulation
technique for solving high-dimensional problems of mathematical physics
concentrated around the two main topics which are deeply related via the
inner need of stochastic description.
1. Development of new Random Walk methods for solving classical
boundary value problems of high dimension not admiting conventional prob-
abilistic representations which is known as an extremely challenging problem
in stochastic analysis. Important examples are the static elasticity problems,
diffraction and Maxwell equations, and system of nonlinear elliptic equations
bustion processes.
2. Development of stochastic models and Monte Carlo simulation tech-
nique for transport processes in stochastic and turbulent flows. The field of
interest includes the transport in the turbulent atmosphere, in rivers, and
in porous media. General challenging problem is to determine the area of
applicability of classical transport equations based on heuristical closure as-
sumptions, and suggest an alternative stochastic Lagrangian model free of
those restrictions. Important features of stochastic Lagrangian methods are
the grid free structure, and convenience for solving high-dimensional applied
problems like the Footprint problem in the forest environment studies, and
the admixture transport in w