Memoirs of My Research on Stochastic Analysis
Kiyosi Itô ................................................... 1
Itô Calculus and Quantum White Noise Calculus
Luigi Accardi, Andreas Boukas ................................ 7
Homogenization of Diffusions on the Lattice Zd with Periodic
Drift Coefficients, Applying a Logarithmic Sobolev Inequality
or a Weak Poincare Inequality
Sergio Albeverio, M. Simonetta Bernabei, Michael Röckner,
Minoru W. Yoshida ............................................ 53
Theory and Applications of Infinite Dimensional Oscillatory
Integrals
Sergio Albeverio, Sonia Mazzucchi ............................ 73
Ambit Processes; with Applications to Turbulence and Tumour
Growth
Ole E. Вarndorff-Nielsen, Jürgen Schmiegel .................. 93
A Stochastic Control Approach to a Robust Utility
Maximization Problem
Giuliana Bordigoni, Anis Matoussi, Martin Schweizer ........ 125
Extending Markov Processes in Weak Duality by Poisson
Point Processes of Excursions
Zhen-Qing Chen, Masatoshi Fukushima, Jiangang Ying ......... 153
Hedging with Options in Models with Jumps
Rama Cont, Peter Tankov, Ekaterina Voltchkova .............. 197
Power Variation Analysis of Some Integral Long-Memory
Processes
José Manuel Corcuera ....................................... 219
Kolmogorov Equations for Stochastic PDE's with
Multiplicative Noise
Giuseppe Da Prato .......................................... 235
Stochastic Integrals and Adjoint Derivatives
Giulia Di Nunno, Yuri A. Rozanov ........................... 265
An Application of Probability to Nonlinear Analysis
Eugene B. Dynkin ........................................... 309
The Space of Stochastic Differential Equations
K. David Elworthy .......................................... 327
Extremes of supOU Processes
Vicky Fasen, Claudia Klüppelberg ........................... 339
Gaussian Bridges
Dario Gasbarra, Tommi Sottinen, Esko Valkeila .............. 361
Some of the Recent Topics on Stochastic Analysis
Takeyuki Hida .............................................. 383
Differential Equations Driven by Holder Continuous Functions
of Order Greater than 1/2
Yaozhong Нu, David Nualart ................................. 399
On Asymptotics of Banach Space-valued Itô Functionals of
Brownian Rough Paths
Yuzuru Inahama, Hiroshi Kawabi ............................. 415
Continuous-Time Markowitz's Problems in an Incomplete
Market, with No-Shorting Portfolios
Hanqing Jin, Xun Yu Zhou ................................... 435
Quantum and Classical Conserved Quantities: Martingales,
Conservation Laws and Constants of Motion
Torbjørn Kolsrud ........................................... 461
Different Lattice Approximations for Hoegh-Krohn's Quantum
Field Model
Song Liang ................................................. 493
Itô Atlas, its Application to Mathematical Finance
and to Exponentiation of Infinite Dimensional Lie Algebras
Paul Malliavin ............................................. 501
The Invariant Distribution of a Diffusion: Some New Aspects
Henry P. McKean ............................................ 515
Formation of Singularities in Madelung Fluid: A
Nonconventional Application of Itô Calculus to Foundations
of Quantum Mechanics
Laura M. Morato ............................................ 527
G-Expectation, G-Brownian Motion and Related Stochastic
Calculus of ô Type
Shige Peng ................................................. 541
Perpetual Integral Functionals of Diffusions and their
Numerical Computations
Paavo Salminen, Olli Wallin ................................ 569
Chaos Expansions and Malliavin Calculus for Levy Processes
Josep Lluís Solé, Frederic Utzet, Josep Vives .............. 595
Study of Simple but Challenging Diffusion Equation
Daniel W. Stroock .......................................... 613
Itô Calculus and Malliavin Calculus
Shinzo Watanabe ............................................ 623
The Malliavin Calculus for Processes with Conditionally
Independent Increments
Aleh L. Yablonski .......................................... 641
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