Published: Springer Verlag, 2007
Description:
1 online resource (xi, 678 pages) : color portraits.
Contents:
“…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 Itô Type -- 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.…”
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