This book describes a completely novel mathematical development which has already
influenced probability theory and has potential for application to engineering and to areas of …

A. The title is designed to indicate those particular aspects of stochastic differential
equations which will be considered here: these are almost equally valid when the manifold …

Let M be a compact manifold without boundary, o be a fixed base point in M, g be a
Riemannian metric on M, and▽ be a g-compatible covariant derivative on TM—the tangent …

Considerons une variete compacte orientable M. Supposons qu'elle soit munie d'un groupe
periodique de diffeornorphisrnes. L'exemple typique est la sphere lorsqu'on la fait tourner le …

The results in Driver [13] for quasi-invariance of Wiener measure on the path space of a
compact Riemannian manifold (M) are extended to the case of pinned Wiener measure. To …

We define the universal cover of the Brownian bridge of a symplectic manifold. This allows
us to define a non-trivial functional over it called the stochastic symplectic action, and to …

Abstract Considers the stochastic Levy Laplacian and Yang-Mills equation on manifolds.
Intrinsic generalization of the non-Abelian Stokes theorem; Introduction of a linear bundle …

We prove some new results on quasi-regular Dirichlet forms. These include results on
perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness …

Integration by parts formulas and rotationally invariant Sobolev calculus on free loop spaces
Page 1 jOURNAL OF Journal of Geometryand Physics 11(1993) 517—528 GE~111~1YAND …

We consider a based loop group L e (G) over a compact Lie groupG, endowed with its
pinned Wiener measureν (the law of the Brownian bridge onG) and we shall calculate the …