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Books > Science & Mathematics > Mathematics > Applied mathematics > Stochastics
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Dynamics of Stochastic Systems (Paperback, New)
Loot Price: R1,950
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Dynamics of Stochastic Systems (Paperback, New)
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Fluctuating parameters appear in a variety of physical systems and
phenomena. They typically come either as random forces/sources, or
advecting velocities, or media (material) parameters, like
refraction index, conductivity, diffusivity, etc. The well known
example of Brownian particle suspended in fluid and subjected to
random molecular bombardment laid the foundation for modern
stochastic calculus and statistical physics. Other important
examples include turbulent transport and diffusion of
particle-tracers (pollutants), or continuous densities (''oil
slicks''), wave propagation and scattering in randomly
inhomogeneous media, for instance light or sound propagating in the
turbulent atmosphere.
Such models naturally render to statistical description, where the
input parameters and solutions are expressed by random processes
and fields.
The fundamental problem of stochastic dynamics is to identify the
essential characteristics of system (its state and evolution), and
relate those to the input parameters of the system and initial
data.
This raises a host of challenging mathematical issues. One could
rarely solve such systems exactly (or approximately) in a closed
analytic form, and their solutions depend in a complicated implicit
manner on the initial-boundary data, forcing and system's (media)
parameters . In mathematical terms such solution becomes a
complicated "nonlinear functional" of random fields and processes.
Part I gives mathematical formulation for the basic physical models
of transport, diffusion, propagation and develops some analytic
tools.
Part II sets up and applies the techniques of variational calculus
and stochastic analysis, like Fokker-Plank equation to those
models, to produce exact or approximate solutions, or in worst case
numeric procedures. The exposition is motivated and demonstrated
with numerous examples.
Part III takes up issues for the coherent phenomena in stochastic
dynamical systems, described by ordinary and partial differential
equations, like wave propagation in randomly layered media
(localization), turbulent advection of passive tracers
(clustering).
Each chapter is appended with problems the reader to solve by
himself (herself), which will be a good training for independent
investigations.
.This book is translation from Russian and is completed with new
principal results of recent research.
.The book develops mathematical tools of stochastic analysis, and
applies them to a wide range of physical models of particles,
fluids, and waves.
.Accessible to a broad audience with general background in
mathematical physics, but no special expertise in stochastic
analysis, wave propagation or turbulence"
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