Advances in analysis : problems of integration
M. S. Burgin
Abstract
M. S. Burgin
Abstract
Preface Introduction: Integration as a basic operation Stochastic transfer principle for multiple integrals with respect to Gaussian random fields with applications Infinite-dimensional Integration, Feynman Integral, & Hyperintegration Simple formulas for conditional function space integrals & applications Functional Derivatives, Schrodinger Equations, & Feynman Integral Path Integrals for Gaussian Process Lower Bounds for Jung Constants of Orlicz Function Spaces Constructive Representation Theory for the Feynman operator calculus on Banach spaces Feynman's operational calculi: Auxiliary Operations & Related Disentangling Formulas Feynman's Operational Calculi: Auxiliary Operations & Related Disentangling Formulas An Integral Equation for Feynman's Operational Calcului Finite Difference Approximation of Quantum Mechanical Wave Packets Functional Integration for Quantum Field Theory Viscosity solutions, backward stochastic differential equations & Markov processes A Fredholm-type theorem for linear integral equations of Stieltjes type The refinement integral: with applications to information theory & statistics On Generalized Product Saks-Heinstok Lemma A generalized Black-Scholes equation without Ito calculus Index.
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Preface Introduction: Integration as a basic operation Stochastic transfer principle for multiple integrals with respect to Gaussian random fields with applications Infinite-dimensional Integration, Feynman Integral, & Hyperintegration Simple formulas for conditional function space integrals & applications Functional Derivatives, Schrodinger Equations, & Feynman Integral Path Integrals for Gaussian Process Lower Bounds for Jung Constants of Orlicz Function Spaces Constructive Representation Theory for the Feynman operator calculus on Banach spaces Feynman's operational calculi: Auxiliary Operations & Related Disentangling Formulas Feynman's Operational Calculi: Auxiliary Operations & Related Disentangling Formulas An Integral Equation for Feynman's Operational Calcului Finite Difference Approximation of Quantum Mechanical Wave Packets Functional Integration for Quantum Field Theory Viscosity solutions, backward stochastic differential equations & Markov processes A Fredholm-type theorem for linear integral equations of Stieltjes type The refinement integral: with applications to information theory & statistics On Generalized Product Saks-Heinstok Lemma A generalized Black-Scholes equation without Ito calculus Index.
Key concepts: Mathematics, Feynman diagram, Path integral formulation, Functional integration, Gaussian integral, Quantum stochastic calculus, Integral equation, Riemann integral