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Global and Stochastic Analysis with Applications to Mathematical Physics

Global and Stochastic Analysis with Applications to Mathematical Physics PDF Author: Yuri E. Gliklikh
Publisher: Springer Science & Business Media
ISBN: 0857291637
Category : Mathematics
Languages : en
Pages : 454

Book Description
Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

Global and Stochastic Analysis with Applications to Mathematical Physics

Global and Stochastic Analysis with Applications to Mathematical Physics PDF Author: Yuri E. Gliklikh
Publisher: Springer Science & Business Media
ISBN: 0857291637
Category : Mathematics
Languages : en
Pages : 454

Book Description
Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems. This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation. Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics. A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics.

Nonstandard Methods in Stochastic Analysis and Mathematical Physics

Nonstandard Methods in Stochastic Analysis and Mathematical Physics PDF Author: Sergio Albeverio
Publisher: Courier Dover Publications
ISBN: 0486468992
Category : Mathematics
Languages : en
Pages : 529

Book Description
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." — Bulletin of the American Mathematical Society. 1986 edition.

New Trends in Stochastic Analysis and Related Topics

New Trends in Stochastic Analysis and Related Topics PDF Author: Huaizhong Zhao
Publisher: World Scientific
ISBN: 9814360910
Category : Mathematics
Languages : en
Pages : 458

Book Description
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

Stochastic Numerics for Mathematical Physics

Stochastic Numerics for Mathematical Physics PDF Author: Grigori N. Milstein
Publisher: Springer Nature
ISBN: 3030820408
Category : Computers
Languages : en
Pages : 754

Book Description
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.

Stochastic Analysis, Stochastic Systems, and Applications to Finance

Stochastic Analysis, Stochastic Systems, and Applications to Finance PDF Author: Allanus Hak-Man Tsoi
Publisher: World Scientific
ISBN: 9814355712
Category : Business & Economics
Languages : en
Pages : 274

Book Description
Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin

Stochastic Analysis on Manifolds

Stochastic Analysis on Manifolds PDF Author: Elton P. Hsu
Publisher: American Mathematical Soc.
ISBN: 0821808028
Category : Mathematics
Languages : en
Pages : 297

Book Description
Mainly from the perspective of a probabilist, Hsu shows how stochastic analysis and differential geometry can work together for their mutual benefit. He writes for researchers and advanced graduate students with a firm foundation in basic euclidean stochastic analysis, and differential geometry. He does not include the exercises usual to such texts, but does provide proofs throughout that invite readers to test their understanding. Annotation copyrighted by Book News Inc., Portland, OR.

Stochastic Processes

Stochastic Processes PDF Author: Wolfgang Paul
Publisher: Springer Science & Business Media
ISBN: 3319003275
Category : Science
Languages : en
Pages : 288

Book Description
This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

Mathematics + Physics

Mathematics + Physics PDF Author: Ludwig Streit
Publisher: World Scientific
ISBN: 9789971978402
Category : Science
Languages : en
Pages : 358

Book Description
This volume focuses on differential equations such as for hydrodynamics, solitary waves, relativistic field theory, stochastic analysis, as well as their interplay, which has been attracting a growing interest in recent years.

Recent Development In Stochastic Dynamics And Stochastic Analysis

Recent Development In Stochastic Dynamics And Stochastic Analysis PDF Author: Jinqiao Duan
Publisher: World Scientific
ISBN: 981446760X
Category : Mathematics
Languages : en
Pages : 306

Book Description
Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also to scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics.The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.

Quantum Stochastic Processes and Noncommutative Geometry

Quantum Stochastic Processes and Noncommutative Geometry PDF Author: Kalyan B. Sinha
Publisher: Cambridge University Press
ISBN: 1139461699
Category : Mathematics
Languages : en
Pages : 301

Book Description
The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.