Itô’s Stochastic Calculus and Probability Theory

Abstract

Levy measure of superprocesses Absorption processes.- A class of integration by parts formulae in stochastic analysis I.- Smooth measures and continuous additive functionals of right Markov processes.- On the decomposition of additive functionals of reflecting Brownian motions.- Equilibrium fluctuations for lattice gas.- Hall's transform and the Segal-Bargmann map.- Lagrangian for pinned diffusion process.- Short time asymptotics and an approximation for the heat kernel of a singular diffusion.- Van Vleck-Pauli formula for Wiener integrals and Jacobi fields.- Some recent developments in nonlinear filtering theory.- Detecting a single defect in a scenery by observing the scenery along a random walk path.- Analytic approach to Yor's formula of exponential additive functionals of Brownian motion.- Stochastic differential equations with jumps and stochastic flows of diffeomorphisms.- A remark on American securities.- Calculus for multiplicative functionals, Ito's formula and differential equations.- A Martin boundary connected with the ?-volume limit of the focussing cubic Schrodinger equation.- Diffusion processes on an open time interval and their time reversal.- On sensitive control and differential games in infinite dimensional space.- Decomposition at the maximum for excursions and bridges of one-dimensional diffusions.- Interacting diffusion systems over Zd.- A Kahler metric on a based loop group and a covariant differentiation.- Burgers system driven by a periodic stochastic flow.- An estimate on the Hessian of the heat kernel.- Environment-wise central limit theorem for a diffusion in a Brownian environment with large drift.- The complex story of simple exclusion.- Levy's stochastic area formula and Brownian motion on compact Lie groups.- Principal values of Brownian local times and their related topics.