Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.
A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sections discussing complex (conformal) martingales and Kahler diffusions have been added.
Inhalt
Preliminaries. Stochastic Integrals and Itô's Formula. Stochastic Calculus. Stochastic Differential Equations. Diffusion Process on Manifolds. Theorems on Comparison and Approximation and their Applications. Bibliography. Index.