Gaussian Hilbert Spaces

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Author: Svante Janson

Publisher: Cambridge University Press

ISBN: 9780521561280

Category: Mathematics

Page: 340

View: 2382

This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.

Stochastic Analysis and Applications to Finance

Essays in Honour of Jia-an Yan

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Author: Tusheng Zhang,Xunyu Zhou

Publisher: World Scientific

ISBN: 9814489158

Category: Mathematics

Page: 464

View: 1622

This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory. It will be a very useful book for young researchers who want to learn about the research directions in the area, as well as experienced researchers who want to know about the latest developments in the area of stochastic analysis and mathematical finance. Contents:Non-Linear Evolution Equations Driven by Rough Paths (Thomas Cass, Zhongmin Qian and Jan Tudor)Optimal Stopping Times with Different Information Levels and with Time Uncertainty (Arijit Chakrabarty and Xin Guo)Finite Horizon Optimal Investment and Consumption with CARA Utility and Proportional Transaction Costs (Yingshan Chen, Min Dai and Kun Zhao)MUniform Integrability of Exponential Martingales and Spectral Bounds of Non-Local Feynman-Kac Semigroups (Zhen-Qing Chen)Continuous-Time Mean-Variance Portfolio Selection with Finite Transactions (Xiangyu Cui, Jianjun Gao and Duan Li)Quantifying Model Uncertainties in the Space of Probability Measures (J Duan, T Gao and G He)A PDE Approach to Multivariate Risk Theory (Robert J Elliott, Tak Kuen Siu and Hailiang Yang)Stochastic Analysis on Loop Groups (Shizan Fang)Existence and Stability of Measure Solutions for BSDE with Generators of Quadratic Growth (Alexander Fromm, Peter Imkeller and Jianing Zhang)Convex Capital Requirements for Large Portfolios (Hans Föllmer and Thomas Knispel)The Mixed Equilibrium of Insider Trading in the Market with Rational Expected Price (Fuzhou Gong and Hong Liu)Some Results on Backward Stochastic Differential Equations Driven by Fractional Brownian Motions (Yaozhong Hu, Daniel Ocone and Jian Song)Potential Theory of Subordinate Brownian Motions Revisited (Panki Kim, Renming Song and Zoran Vondraček)Research on Social Causes of the Financial Crisis (Steven Kou)Wick Formulas and Inequalities for the Quaternion Gaussian and β-Permanental Variables (Wenbo V Li and Ang Wei)Further Study on Web Markov Skeleton Processes (Yuting Liu, Zhi-Ming Ma and Chuan Zhou)MLE of Parameters in the Drifted Brownian Motion and Its Error (Lemee Nakamura and Weian Zheng)Optimal Partial Information Control of SPDEs with Delay and Time-Advanced Backward SPDEs (Bernt Øksendal, Agnès Sulem and Tusheng Zhang)Simulation of Diversified Portfolios in Continuous Financial Markets (Eckhard Platen and Renata Rendek)Coupling and Applications (Feng-Yu Wang)SDEs and a Generalised Burgers Equation (Jiang-Lun Wu and Wei Yang)Mean-Variance Hedging in the Discontinuous Case (Jianming Xia) Readership: Graduates and researchers in stochatic analysis and mathematical finance. Keywords:Stochastic Analysis;Finance;Stochastic Partial Differential Equations;Backward Stochastic Differential Equations;Potential TheoryKey Features:Unique combination of stochastic analysis and financeSolicited articles from leading researchers in the areaA volume in honour of Jia-an Yan, a prominent scholar in both stochastic analysis and mathematical finance

Zeros of Gaussian Analytic Functions and Determinantal Point Processes

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Author: John Ben Hough,Manjunath Krishnapur ,Yuval Peres ,B\'alint Vir\'ag

Publisher: American Mathematical Soc.

ISBN: 0821843737

Category: Mathematics

Page: 154

View: 1128

The book examines in some depth two important classes of point processes, determinantal processes and ``Gaussian zeros'', i.e., zeros of random analytic functions with Gaussian coefficients. These processes share a property of ``point-repulsion'', where distinct points are less likely to fall close to each other than in processes, such as the Poisson process, that arise from independent sampling. Nevertheless, the treatment in the book emphasizes the use of independence: for random power series, the independence of coefficients is key; for determinantal processes, the number of points in a domain is a sum of independent indicators, and this yields a satisfying explanation of the central limit theorem (CLT) for this point count. Another unifying theme of the book is invariance of considered point processes under natural transformation groups. The book strives for balance between general theory and concrete examples. On the one hand, it presents a primer on modern techniques on the interface of probability and analysis. On the other hand, a wealth of determinantal processes of intrinsic interest are analyzed; these arise from random spanning trees and eigenvalues of random matrices, as well as from special power series with determinantal zeros. The material in the book formed the basis of a graduate course given at the IAS-Park City Summer School in 2007; the only background knowledge assumed can be acquired in first-year graduate courses in analysis and probability.

Diffusion, Quantum Theory, and Radically Elementary Mathematics. (MN-47)

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Author: William G. Faris

Publisher: Princeton University Press

ISBN: 1400865255

Category: Mathematics

Page: 256

View: 9502

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Concentration, Functional Inequalities, and Isoperimetry

International Workshop on Concentration, Functional Inequalities, and Isoperimetry, October 29-November 1, 2009, Florida Atlantic University, Boca Raton, Florida

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Author: Christian Houdré

Publisher: American Mathematical Soc.

ISBN: 0821849719

Category: Mathematics

Page: 211

View: 9691

The volume contains the proceedings of the international workshop on Concentration, Functional Inequalities and Isoperimetry, held at Florida Atlantic University in Boca Raton, Florida, from October 29-November 1, 2009. The interactions between concentration, isoperimetry and functional inequalities have led to many significant advances in functional analysis and probability theory. Important progress has also taken place in combinatorics, geometry, harmonic analysis and mathematical physics, to name but a few fields, with recent new applications in random matrices and information theory. This book should appeal to graduate students and researchers interested in the fascinating interplay between analysis, probability, and geometry.

Forthcoming Books

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Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3590

Normal Approximations with Malliavin Calculus

From Stein's Method to Universality

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Author: Ivan Nourdin,Giovanni Peccati

Publisher: Cambridge University Press

ISBN: 1107017777

Category: Mathematics

Page: 239

View: 4440

This book shows how quantitative central limit theorems can be deduced by combining two powerful probabilistic techniques: Stein's method and Malliavin calculus.

Proceedings of the International Congress of Mathematicians

Madrid, August 22-30, 2006

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Author: Marta Sanz Solé

Publisher: Amer Mathematical Society

ISBN: 9783037190227

Category: Mathematics

Page: 4500

View: 8704

The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.

Books in Print

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3762

Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Probability on Real Lie Algebras

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Author: Uwe Franz,Nicolas Privault

Publisher: Cambridge University Press

ISBN: 110712865X

Category: Mathematics

Page: 302

View: 3715

This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.

The Lévy Laplacian

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Author: M. N. Feller

Publisher: Cambridge University Press

ISBN: 9781139447966

Category: Mathematics

Page: N.A

View: 7823

The Lévy Laplacian is an infinite-dimensional generalization of the well-known classical Laplacian. The theory has become well developed in recent years and this book was the first systematic treatment of the Lévy–Laplace operator. The book describes the infinite-dimensional analogues of finite-dimensional results, and more especially those features which appear only in the generalized context. It develops a theory of operators generated by the Lévy Laplacian and the symmetrized Lévy Laplacian, as well as a theory of linear and nonlinear equations involving it. There are many problems leading to equations with Lévy Laplacians and to Lévy–Laplace operators, for example superconductivity theory, the theory of control systems, the Gauss random field theory, and the Yang–Mills equation. The book is complemented by an exhaustive bibliography. The result is a work that will be valued by those working in functional analysis, partial differential equations and probability theory.