β Scribed by Malliavin, Paul
No coin nor oath required. For personal study only.
This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.
Front Matter....Pages I-XI
Front Matter....Pages 1-2
Gaussian Probability Spaces....Pages 3-27
Gross-Stroock Sobolev Spaces over a Gaussian Probability Space....Pages 29-62
Smoothness of Laws....Pages 63-83
Front Matter....Pages 87-88
Foundations of Quasi-Sure Analysis: Hierarchy of Capacities and Precise Gaussian Probability Spaces....Pages 89-123
Differential Geometry on a Precise Gaussian Probability Space....Pages 125-144
Front Matter....Pages 147-148
White Noise Stochastic Integrals as Divergences....Pages 149-171
ItΓ΄βs Theory of Stochastic Integration....Pages 173-198
Front Matter....Pages 201-202
From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle....Pages 203-235
Elliptic Estimates Through Stochastic Analysis....Pages 237-251
Front Matter....Pages 257-258
Stochastic Analysis on Wiener Spaces....Pages 259-271
Path Spaces and Their Tangent Spaces....Pages 273-298
Back Matter....Pages 301-346
Stochastic analysis
π SIMILAR VOLUMES
Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, non-linear functional analysis, control theory and statistical mechanics.
Stochastic analysis is often understood as the analysis of functionals defined on the Wiener space, i.e., the space on which the Wiener process is realized. Since the Wiener space is infinite-dimensional, it requires a special calculus, the so-called Malliavin calculus. This book provides readers wi
This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (part
<p><p>This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales