Integration in Function Spaces and Some of Its Applications |
Contents
Section 1 Introduction | 5 |
Section 2 Construction of the Wiener measure and integration of some simple functionals | 7 |
Section 3 Elements of probabilistic potential theory | 23 |
8 other sections not shown
Common terms and phrases
analogue assignment of measures asymptotic behavior axiom boundary condition Brownian motion Brownian paths calculate classical path continuous functions converges d(path defined denotes derivation differential equation Donsker-Varadhan dt ds Eexp eigen eigenfunctions eigenvalues elementary sets equivalent ergodic Feynman's formula function spaces hence independent Gaussian variables initial condition integral equation integration in function interval K(xox kernel Lebesgue measure linear combinations Markov chain matrix mean zero measure theoretic non-negative P(ij particle path integral probabilistic Probabilistic Potential Theory problem purely analytic Q(xox Quantum Mechanics regularity conditions result Riccati equation satisfies scattering length Schrödinger equation SECTION So(t space of continuous theorem theory of Brownian To(y Va(y Vo(y VV(y Wiener integral Wiener measure Wiener process zero and variance αξ απ αρ ατ βη ΓΕΩ ΕΩ ίξ κλ λη λι ναι Σπ ΩΩ дхо дх