Stochastic Analysis and Applications (eBook)

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

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