Ebook: Stochastic Analysis and Applications: The Abel Symposium 2005

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.

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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. This volume combines both papers from the invited speakers and contributions by the presenting lecturers. In addition, it includes the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.

---

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. This volume combines both papers from the invited speakers and contributions by the presenting lecturers. In addition, it includes the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.

Content:
Front Matter....Pages I-XI
Memoirs of My Research on Stochastic Analysis....Pages 1-6
It? Calculus and Quantum White Noise Calculus....Pages 7-51
Homogenization of Diffusions on the Lattice Zd with Periodic Drift Coefficients, Applying a Logarithmic Sobolev Inequality or a Weak Poincar? Inequality....Pages 53-72
Theory and Applications of Infinite Dimensional Oscillatory Integrals....Pages 73-91
Ambit Processes; with Applications to Turbulence and Tumour Growth....Pages 93-124
A Stochastic Control Approach to a Robust Utility Maximization Problem....Pages 125-151
Extending Markov Processes in Weak Duality by Poisson Point Processes of Excursions....Pages 153-196
Hedging with Options in Models with Jumps....Pages 197-217
Power Variation Analysis of Some Integral Long-Memory Processes....Pages 219-234
Kolmogorov Equations for Stochastic PDE's with Multiplicative Noise....Pages 235-263
Stochastic Integrals and Adjoint Derivatives....Pages 265-307
An Application of Probability to Nonlinear Analysis....Pages 309-325
The Space of Stochastic Differential Equations....Pages 327-337
Extremes of supOU Processes....Pages 339-359
Gaussian Bridges....Pages 361-382
Some of the Recent Topics on Stochastic Analysis....Pages 383-397
Differential Equations Driven by H?lder Continuous Functions of Order Greater than 1/2....Pages 399-413
On Asymptotics of Banach Space-valued It? Functionals of Brownian Rough Paths....Pages 415-434
Continuous-Time Markowitz's Problems in an Incomplete Market, with No-Shorting Portfolios....Pages 435-459
Quantum and Classical Conserved Quantities: Martingales, Conservation Laws and Constants of Motion....Pages 461-491
Different Lattice Approximations for H?egh-Krohn's Quantum Field Model....Pages 493-499
It? Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras....Pages 501-514
The Invariant Distribution of a Diffusion: Some New Aspects....Pages 515-526
Formation of Singularities in Madelung Fluid: A Nonconventional Application of It? Calculus to Foundations of Quantum Mechanics....Pages 527-540
Perpetual Integral Functionals of Diffusions and their Numerical Computations....Pages 541-567
Chaos Expansions and Malliavin Calculus for L?vy Processes....Pages 569-594
Study of Simple but Challenging Diffusion Equation....Pages 595-612
It? Calculus and Malliavin Calculus....Pages 613-621
The Malliavin Calculus for Processes with Conditionally Independent Increments....Pages 623-639
....Pages 641-678