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Stochastic Numerics for Mathematical Physics (Paperback, 2nd ed. 2021)
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Stochastic Numerics for Mathematical Physics (Paperback, 2nd ed. 2021)
Series: Scientific Computation
Expected to ship within 10 - 15 working days
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This book is a substantially revised and expanded edition
reflecting major developments in stochastic numerics since the
first edition was published in 2004. The new topics, in particular,
include mean-square and weak approximations in the case of
nonglobally Lipschitz coefficients of Stochastic Differential
Equations (SDEs) including the concept of rejecting trajectories;
conditional probabilistic representations and their application to
practical variance reduction using regression methods; multi-level
Monte Carlo method; computing ergodic limits and additional classes
of geometric integrators used in molecular dynamics; numerical
methods for FBSDEs; approximation of parabolic SPDEs and nonlinear
filtering problem based on the method of characteristics. SDEs have
many applications in the natural sciences and in finance. Besides,
the employment of probabilistic representations together with the
Monte Carlo technique allows us to reduce the solution of
multi-dimensional problems for partial differential equations to
the integration of stochastic equations. This approach leads to
powerful computational mathematics that is presented in the
treatise. Many special schemes for SDEs are presented. In the
second part of the book numerical methods for solving complicated
problems for partial differential equations occurring in practical
applications, both linear and nonlinear, are constructed. All the
methods are presented with proofs and hence founded on rigorous
reasoning, thus giving the book textbook potential. An overwhelming
majority of the methods are accompanied by the corresponding
numerical algorithms which are ready for implementation in
practice. The book addresses researchers and graduate students in
numerical analysis, applied probability, physics, chemistry, and
engineering as well as mathematical biology and financial
mathematics.
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