Analysis on Wiener Space and Applications

2010/03/08 by Ali Süleyman Üstünel, Üstünel, A. S. · 6 citations
Mathematics · Economics, Econometrics and Finance · #advanced mathematical theories #Stochastic processes and financial applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1003.1649

Abstract

The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of Paul Malliavin.

Citations

• The geometry of optimal transportation
• Polar factorization and monotone rearrangement of vector‐valued functions
• Logarithmic Sobolev Inequalities

Cited by

• On the quasi-invariance of the Wiener measure on path spaces and the anticipative integrals over a Riemannian manifold
• Stein's method for diffusive limit of queueing processes
• On the short-time behaviour of up-and-in barrier options using Malliavin calculus
• Upper bounds for the density of solutions of stochastic differential equations driven by fractional Brownian motions
• Causal transference plans and their Monge-Kantorovich problems
• Strong solutions of SDE's with rough coefficients

Related

• Curved Wiener Space Analysis
• Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space
• An introduction to BV functions in Wiener spaces
• Towards Abstract Wiener Model Spaces
• Topics in Gaussian Wiener chaos expansion