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Stochastic Numerics for Mathematical Physics
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 no...
Stochastic Numerics for Mathematical Physics
Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. 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, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
Stochastic Stability of Differential Equations
Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.
Numerical Integration of Stochastic Differential Equations
This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.
Lithuanian Jewish Communities
This volume lists, in alphabetical order, the major Jewish communities that existed in Lithuania before World War II. The name of each community is accompanied by information about it: when it was founded, the Jewish population in different years, shops and synagogues, and the names of citizens. An appendix locates each town on a map of Lithuania. Since most of the Jewish communities in Lithuania were destroyed in the Holocaust, this volume will be a valuable tool in recreating a picture of Lithuanian Jewry.
The Golden Age of Jewish Achievement
The stunning performance of Jews over the last 125 years can only be compared with that of the Italians during the Renaissance, the Greeks during the era of Pericles, or the Dutch during their own Golden Age. The Golden Age details that record in more than 60 exhibits covering the range from Nobel prizes to Rock 'n' Roll Hall of Fame awards, from Pulitzer Prizes to chess champions, from philanthropy to Supreme Court Justices and more. But more intriguing is the question, "Why has this happened?" (the question posed by Rabbi Harold N. Kushner, author of When Bad Things Happen to Good People).
The Chosen People
"Einstein... Shylock... Rothschild... Trotsky... Jesus. The scientist and philosopher... the greedy money-lender and middle man... the impoverished immigrant... the elite of politics and high finance... the prophet... the revolutionary. All of these have been faces of the Jewish people over the centuries. They have inspired admiration, envy, suspicion, and hatred and overflowed with world-changing personages. The historian Yuri Slezkine claimed that the 20th century was nothing less than the 'Jewish century,' so indispensable were they in the creation of the modern world"--Cover, p. [4].
Fundamentals of Computational Fluid Dynamics
The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.
A Computational Method in Plasma Physics
In this book, we report on research in methods of computational magneto hydrodynamics supported by the United States Department of Energy under Contract EY-76-C-02-3077 with New York University. The work has re sulted in a computer code for mathematical analysis of the equilibrium and stability of a plasma in three dimensions with toroidal geometry but no sym metry. The code is listed in the final chapter. Versions of it have been used for the design of experiments at the Los Alamos Scientific Laboratory and the Max Planck Institute for Plasma Physics in Garching. We are grateful to Daniel Barnes, Jeremiah Brackbill, Harold Grad, William Grossmann, Abraham Kadish, Peter Lax, Guthrie Miller, ...
