Lindstrom / Øksendal / Zhang Stochastic Analysis and Applications

The Abel Symposium 2005
1. Auflage 2007
ISBN: 978-3-540-70847-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 678 Seiten

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.

Autoren/Hrsg.

Lindstrom, Tom

Øksendal, Bernt

Zhang, Tusheng

Inhaltsverzeichnis

1;Preface to the Series;6
2;Preface;8
3;Contents;10
4;Memoirs of My Research on Stochastic Analysis;13
5;Itˆo Calculus and Quantum White Noise Calculus;18
6;Homogenization of Diffusions on the Lattice Zd with Periodic Drift Coefficients, Applying a Logarithmic Sobolev Inequality or a Weak Poincare Inequality;63
7;Theory and Applications of Infinite Dimensional Oscillatory Integrals;83
8;Ambit Processes; with Applications to Turbulence and Tumour Growth;102
9;A Stochastic Control Approach to a Robust Utility Maximization Problem;134
10;Extending Markov Processes in Weak Duality by Poisson Point Processes of Excursions;161
11;Hedging with Options in Models with Jumps;205
12;Power Variation Analysis of Some Integral Long- Memory Processes;226
13;Kolmogorov Equations for Stochastic PDE’s with Multiplicative Noise;242
14;Stochastic Integrals and Adjoint Derivatives;271
15;An Application of Probability to Nonlinear Analysis;314
16;The Space of Stochastic Differential Equations;331
17;Extremes of supOU Processes;342
18;Gaussian Bridges;363
19;Some of the Recent Topics on Stochastic Analysis;385
20;Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/ 2;400
21;On Asymptotics of Banach Space-valued Ito Functionals of Brownian Rough Paths;415
22;Continuous-Time Markowitz’s Problems in an Incomplete Market, with No- Shorting Portfolios;435
23;Quantum and Classical Conserved Quantities: Martingales, Conservation Laws and Constants of Motion;460
24;Different Lattice Approximations for Høegh- Krohn’s Quantum Field Model;491
25;Ito Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras;498
26;The Invariant Distribution of a Diffusion: Some New Aspects;512
27;Formation of Singularities in Madelung Fluid: A Nonconventional Application of Ito Calculus to Foundations of Quantum Mechanics;524
28;G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itˆo Type;538
29;Perpetual Integral Functionals of Diffusions and their Numerical Computations;565
30;Chaos Expansions and Malliavin Calculus for Levy Processes;591
31;Study of Simple but Challenging Diffusion Equation;609
32;Ito Calculus and Malliavin Calculus;618
33;The Malliavin Calculus for Processes with Conditionally Independent Increments;635