This text provides a systematic exposition of the modern theory of Gaussian measures. It
presents, with complete and detailed proofs, fundamental facts about finite and infinite …

Learn the basics of white noise theory with White Noise Distribution Theory. This book
covers the mathematical foundation and key applications of white noise theory without …

The monograph is devoted mainly to the analytical study of the differential, pseudo-
differential and stochastic evolution equations describing the transition probabilities of …

One of the most challenging problems of modern physics is the connection between the
macroscopic and the microscopic world, that is between classical and quantum mechanics …

An approach to infinite-dimensional integration which unifies the case of oscillatory integrals
and the case of probabilistic type integrals is presented. It provides a truly infinite …

In a largely heuristic but fascinating recent paper, Hu and Meyer have given a" formula" for
the Feynman integral of a random variable $ f $ on Wiener space in terms of the expansion …

It is shown that the unique solution of Ψ (t, x)=-(z^ 2)^ α/2 (-Δ)^ α/2 Ψ (t, x)+ V (z, x) Ψ (t, x),\Ψ
(0, x)= f (x),. can be represented as Ψ (t, x)=\Bbb E f (x+ (z)^ 1/α X_s)\exp\left {\int_0^ t V (z …

A general class of infinite dimensional oscillatory integrals with polynomially growing phase
functions is studied. A representation formula of the Parseval type is proved, as well as a …

The concept of a conditional Feynman integral of a function F given a function X is
introduced, and its existence is established for various functions. Then the conditional …

The time-dependent quartic oscillator—a Feynman path integral approach Page 1 Journal of
Functional Analysis 238 (2006) 471–488 www.elsevier.com/locate/jfa The time-dependent …