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Author: Laurent Decreusefond
Publisher: Springer Science & Business Media
ISBN: 9780817642006
Category : Mathematics
Languages : en
Pages : 266
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Book Description
One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.
Author: Laurent Decreusefond
Publisher: Springer Science & Business Media
ISBN: 9780817642006
Category : Mathematics
Languages : en
Pages : 266
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Book Description
One of the most challenging subjects of stochastic analysis in relation to physics is the analysis of heat kernels on infinite dimensional manifolds. The simplest nontrivial case is that of thepath and loop space on a Lie group. In this volume an up-to-date survey of the topic is given by Leonard Gross, a prominent developer of the theory. Another concise but complete survey of Hausdorff measures on Wiener space and its applications to Malliavin Calculus is given by D. Feyel, one of the most active specialists in this area. Other survey articles deal with short-time asymptotics of diffusion pro cesses with values in infinite dimensional manifolds and large deviations of diffusions with discontinuous drifts. A thorough survey is given of stochas tic integration with respect to the fractional Brownian motion, as well as Stokes' formula for the Brownian sheet, and a new version of the log Sobolev inequality on the Wiener space. Professional mathematicians looking for an overview of the state-of-the art in the above subjects will find this book helpful. In addition, graduate students as well as researchers whose domain requires stochastic analysis will find the original results of interest for their own research. The organizers acknowledge gratefully the financial help ofthe University of Oslo, and the invaluable aid of Professor Bernt 0ksendal and l'Ecole Nationale Superieure des Telecommunications.
Author: Huaizhong Zhao
Publisher: World Scientific
ISBN: 9814360910
Category : Mathematics
Languages : en
Pages : 458
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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.
Author: Michael Falk
Publisher: Birkhäuser
ISBN: 3034877919
Category : Mathematics
Languages : en
Pages : 381
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Book Description
Since the publication of the first edition of this seminar book, the theory and applications of extremes and rare events have seen increasing interest. Laws of Small Numbers gives a mathematically oriented development of the theory of rare events underlying various applications. The new edition incorporates numerous new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.
Author: Vladimir V. Kalashnikov
Publisher: Springer
ISBN: 3540468633
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Traditionally the Stability seminar, organized in Moscow but held in different locations, has dealt with a spectrum of topics centering around characterization problems and their stability, limit theorems, probabil- ity metrics and theoretical robustness. This volume likewise focusses on these main topics in a series of original and recent research articles.
Author: Yaozhong Hu
Publisher: American Mathematical Soc.
ISBN: 0821837044
Category : Mathematics
Languages : en
Pages : 144
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Book Description
A paper that studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.
Author: Hikosaburo Komatsu
Publisher: Springer
ISBN: 3540475656
Category : Mathematics
Languages : en
Pages : 425
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Book Description
In these proceedings of the international conference held in Kyoto in memoryof the late Professor K saku Yosida, twenty six invited speakers display in their many facets of functional analysis and its applications in the research tradition of Yosida's school. Many of the topics are related tolinear and non-linear partial differential equations, including the Schr|dinger equations, the Navier-Stokes equations and quasilinear hyperbolic equations. Several of the papers are survey articles, the others are original (unpublished) and refereed research articles. Also included is a full listing of the publications of K. Yosida. Recommendedto students and research workers looking for a bird's-eye view of current research activity in functional analysis and its applications. FROM THE CONTENTS: K. Ito: Semigroups in probability theory.- T. Kato: Abstract evolution equations, linear and quasilinear, revisited.- J.L. Lions: Remarkson systems with incompletely given initial data and incompletely given part of the boundary.- H. Brezis: New energies for harmonic maps and liquid crystals.- D. Fujiwara: Some Feynman path integrals as oscillatory integrals over a Sobolev manifold.- M. Giga, Y. Giga, H. Sohr: L estimates for the Stokes system.- Y. Kawahigashi: Exactly solvable orbifold models and subfactors.- H. Kitada: Asymptotic completeness of N-body wave operators II. A new proof for the short-range case and the asymptotic clustering for the long-range systems. Y. Kobayashi, S. Oharu: Semigroups oflocally Lipschitzian operators and applications.- H. Komatsu: Operational calculus and semi-groups of operators.
Author: Pierre Picco
Publisher: Springer Science & Business Media
ISBN: 9783764321697
Category : Gardening
Languages : en
Pages : 246
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Book Description
This volume is based on the lecture notes of six courses delivered at a CIMPA Summer School in Temuco, Chile, in January 2001. The courses are: asymptotic of the heat kernel in unbounded domains; spin systems with long range interactions; non-linear Dirichlet problem and non-linear integration; first-passage percolation; central limit theorem for Markov processes; stochastic orders and stopping times in Brownian motion. The level of each course is that of a graduate course, but the material will also be of interest for the specialist.
Author: Geon Ho Choe
Publisher: Springer
ISBN: 3319255894
Category : Mathematics
Languages : en
Pages : 660
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Book Description
This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.
Author: Dominique Bakry
Publisher: Springer
ISBN: 3540485686
Category : Mathematics
Languages : en
Pages : 429
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Book Description
This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequa- lities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survi- val analysis; it includes product-integral theory, Kaplan- Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, loca- lization properties and intermittency. Each of these chap- ters provides an introduction to and survey of its subject.
Author: Szymon Dolecki
Publisher: Springer
ISBN: 3540468676
Category : Mathematics
Languages : en
Pages : 227
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Book Description
The 2-yearly French-German Conferences on Optimization review the state-of-the-art and the trends in the field. The proceedings of the Fifth Conference include papers on projective methods in linear programming (special session at the conference), nonsmooth optimization, two-level optimization, multiobjective optimization, partial inverse method, variational convergence, Newton type algorithms and flows and on practical applications of optimization. A. Ioffe and J.-Ph. Vial have contributed survey papers on, respectively second order optimality conditions and projective methods in linear programming.
