Stochastic Analysis and Applications

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