Sergey V. Lototsky's Books

Mathematics of Physics and Engineering

By: Edward K. Blum,Sergey V. Lototsky

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Mathematics of Physics and Engineering

By: Edward K. Blum,Sergey V. Lototsky

Aimed at scientists and engineers, this book is an exciting intellectual journey through the mathematical worlds of Euclid, Newton, Maxwell, Einstein, and Schrodinger-Dirac.While similar books present the required mathematics in a piecemeal manner with tangential references to the relevant physics and engineering, this textbook serves the interdisciplinary needs of engineers, scientists and applied mathematicians by unifying the mathematics and physics into a single systematic body of knowledge but preserving the rigorous logical development of the mathematics.The authors take an unconventional approach by integrating the mathematics with its motivating physical phenomena and, conversely, by showing how the mathematical models predict new physical phenomena.

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Page Count

500

Publisher

World Scientific

Published Date

ISBN 10

981256621X

ISBN 13

9789812566218

Stochastic Partial Differential Equations

By: Sergey V. Lototsky,Boris L. Rozovsky

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Stochastic Partial Differential Equations

By: Sergey V. Lototsky,Boris L. Rozovsky

Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected to the material discussed at a particular place in the text. The questions usually ask to verify something, so that the reader already knows the answer and, if pressed for time, can move on. Accordingly, no solutions are provided, but there are often hints on how to proceed. The book will be of interest to everybody working in the area of stochastic analysis, from beginning graduate students to experts in the field.

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Page Count

517

Publisher

Springer

Published Date

ISBN 10

3319586475

ISBN 13

9783319586472

Stochastic Differential Equations

Theory and Applications

By: Peter H. Baxendale,Sergey V. Lototsky

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Stochastic Differential Equations

Theory and Applications

By: Peter H. Baxendale,Sergey V. Lototsky

The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract attention of mathematicians of all generations, because, together with a short but thorough introduction to SPDEs, it presents a number of optimal and essentially non-improvable results about solvability for a large class of both linear and non-linear equations.

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Page Count

416

Publisher

World Scientific

Published Date

ISBN 10

9812706623

ISBN 13

9789812706621

Stochastic Evolution Systems

Linear Theory and Applications to Non-Linear Filtering

By: Boris L. Rozovsky,Sergey V. Lototsky

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Stochastic Evolution Systems

Linear Theory and Applications to Non-Linear Filtering

By: Boris L. Rozovsky,Sergey V. Lototsky

This monograph, now in a thoroughly revised second edition, develops the theory of stochastic calculus in Hilbert spaces and applies the results to the study of generalized solutions of stochastic parabolic equations. The emphasis lies on second-order stochastic parabolic equations and their connection to random dynamical systems. The authors further explore applications to the theory of optimal non-linear filtering, prediction, and smoothing of partially observed diffusion processes. The new edition now also includes a chapter on chaos expansion for linear stochastic evolution systems. This book will appeal to anyone working in disciplines that require tools from stochastic analysis and PDEs, including pure mathematics, financial mathematics, engineering and physics.

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Page Count

340

Publisher

Springer

Published Date

ISBN 10

3319948938

ISBN 13

9783319948935

Book's by Sergey V. Lototsky

Mathematics of Physics and Engineering

Mathematics of Physics and Engineering

Stochastic Partial Differential Equations

Stochastic Partial Differential Equations

Stochastic Differential Equations

Stochastic Differential Equations

Stochastic Evolution Systems

Stochastic Evolution Systems

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