Conditional Analytic Feynman Integrals on Abstract Wiener Spaces

Analytic Evaluation of Feynman Graph Integrals *

We review the main steps of the differential equation approach to the analytic evaluation of Feynman graphs, showing at the same time its application to the 3-loop sunrise graph in a particular kinematical configuration. • The differential equation approach to the analytic evaluation of Feynman graph inte-grals applies to loop integrals defined in the by now customary regularization in d contin...

Conditional exponential moments for iterated Wiener integrals

We provide sharp exponential moment bounds for (Stratonovich) iterated stochastic integrals under conditioning by certain small balls, including balls in certain HH older-like norms of exponent greater than 1=3. The proof uses a control of the variation of the L evy area, under conditioning. The results are applied to the computation of the Onsager-Machlup functional of diiusion processes with ...

Computing conditional Wiener integrals of functionals of a general form

A numerical method of second order of accuracy for computing conditional Wiener integrals of smooth functionals of a general form is proposed. The method is based on simulation of Brownian bridge via the corresponding stochastic di¤erential equations (SDEs) and on ideas of the weak-sense numerical integration of SDEs. A convergence theorem is proved. Special attention is paid to integral-type f...

An Infinitesimal Approach to Stochastic Analysis on Abstract Wiener Spaces

Linear Functionals and Integrals in Abstract Spaces

In his addendum to Saks, Theory of the Integral, Banach considers a Lebesgue integral defined in a manner quite similar to that of Daniell and remarks that no use is made of a measure. I t is, however, quite easy to show that Banach's and Daniell's integrals are expressible as Lebesgue integrals whose measure functions are regular outer measures in the sense of Carathéodory. In the first two se...