edited by Ana Bela Cruzeiro (Grupo de Física-Matemática & Universidade Técnica de Lisboa, Portugal) , Habib Ouerdiane (University of Tunis El Manar, Tunisia) , & Nobuaki Obata (Tohoku University, Japan)

Table of Contents (52k)
Preface (51k)
Chapter 1: Geometry and Integration by Parts on H \ Diff (S1) (650k)

This volume highlights recent developments of stochastic analysis with a wide spectrum of applications, including stochastic differential equations, stochastic geometry, and nonlinear partial differential equations.

While modern stochastic analysis may appear to be an abstract mixture of classical analysis and probability theory, this book shows that, in fact, it can provide versatile tools useful in many areas of applied mathematics where the phenomena being described are random. The geometrical aspects of stochastic analysis, often regarded as the most promising for applications, are specially investigated by various contributors to the volume.

• Invariant Measures for Ornstein–Uhlenbeck Operators (H Airault & P Malliavin)
• Backward Stochastic Differential Equations with Respect to Martingales (A R Al-Hussein)
• A Nonlinear Stochastic Equation of Convolution Type (F Cipriano et al.)
• On a Variational Principle for the Navier–Stokes Equation (D A Gomes)
• Characterizations of Standard Noises and Applications (T Hida & Si Si)
• Analysis of Stable White Noise Functionals (YaJ Lee & H-H Shih)
• FKG Inequality on the Wiener Space via Predictable Representation (Y Ma & N Privault)
• Path-Integral Estimates of Ground-State Functionals (R V Mendes)
• Creation and Annihilation Operators on Locally Compact Spaces (W von Waldenfels)
• and other papers