Stochastic Analysis and Applications

by Benth, Fred Espen; Di Nunno, Giulia; Lindstrom, Tom; Oksendal, Bernt; Zhang, Tusheng

• ISBN13: 9783540708469
• ISBN10: 3540708464
• Format: Hardcover
• Copyright: 2007-06-03
• Publisher: Springer Verlag

Summary

Kiyosi Ito, the founder of stochastic calculus, is one of the few central figures of the twentieth century mathematics who reshaped the mathematical world. Today stochastic calculus is a central research field with applications in several other mathematical disciplines, for example physics, engineering, biology, economics and finance. The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over the world were invited to present the newest developments within the exciting and fast growing field of stochastic analysis. The present volume combines both papers from the invited speakers and contributions by the presenting lecturers. A special feature is the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.

Author Biography

Information on the volume editors:All the Editors are working in stochastic analysis. Bernt +ÿksendal received the Nansen Prize in 1996 and was elected member of the Norwegian Academy of Science and Letters in 1996.

Table of Contents

Memoirs of My Research on Stochastic Analysis	p. 1
Itô Calculus and Quantum White Noise Calculus	p. 7
Homogenization of Diffusions on the Lattice Zd with Periodic Drift Coefficients, Applying a Logarithmic Sobolev Inequality or a Weak Poincaré Inequality	p. 53
Theory and Applications of Infinite Dimensional Oscillatory Integrals	p. 73
Ambit Processes; with Applications to Turbulence and Tumour Growth	p. 93
A Stochastic Control Approach to a Robust Utility Maximization Problem	p. 125
Extending Markov Processes in Weak Duality by Poisson Point Processes of Excursions	p. 153
Hedging with Options in Models with Jumps	p. 197
Power Variation Analysis of Some Integral Long-Memory Processes	p. 219
Kolmogorov Equations for Stochastic PDE's with Multiplicative Noise	p. 235
Stochastic Integrals and Adjoint Derivatives	p. 265
An Application of Probability to Nonlinear Analysis	p. 309
The Space of Stochastic Differential Equations	p. 327
Extremes of supOU Processes	p. 339
Gaussian Bridges	p. 361
Some of the Recent Topics on Stochastic Analysis	p. 383
Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/2	p. 399
On Asymptotics of Banach Space-valued Itô Functionals of Brownian Rough Paths	p. 415
Continuous-Time Markowitz's Problems in an Incomplete Market, with No-Shorting Portfolios	p. 435
Quantum and Classical Conserved Quantities: Martingales, Conservation Laws and Constants of Motion	p. 461
Different Lattice Approximations for Hôegh-Krohn's Quantum Field Model	p. 493
Itô Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras	p. 501
The Invariant Distribution of a Diffusion: Some New Aspects	p. 515
Formation of Singularities in Madelung Fluid: A Nonconventional Application of Itô Calculus to Foundations of Quantum Mechanics	p. 527
G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type	p. 541
Perpetual Integral Functionals of Diffusions and their Numerical Computations	p. 569
Chaos Expansions and Malliavin Calculus for Lévy Processes	p. 595
Study of Simple but Challenging Diffusion Equation	p. 613
Itô Calculus and Malliavin Calculus	p. 623
The Malliavin Calculus for Processes with Conditionally Independent Increments	p. 641
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