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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.
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.
- No. of pages:
- © North Holland 1989
- 1st March 1992
- North Holland
- eBook ISBN:
@qu:This book has been eagerly awaited by experts... The authors are to be congratulated on a splendid piece of exposition. @source:Short Book Reviews @qu:...has been carefully constructed and lucidly presented; it will become a standard reference. @source:European Journal of Operational Research @from:A. Georgescu @qu:The book is of much interest for probabilists and geometers and for a wide circle of specialists, in particular scientists and engineers. @source:Revue Roumaine de Mathematique Pure et Applique @from:H. Heyer @qu:All mathematicians who take stochastic differential equations seriously, are encouraged anew to consult this standard work. @source:Metrika