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Stochastic differential equations and diffusion processes

Author: Nobuyuki Ikeda; Shinzo Watanabe
Publisher: Amsterdam ; New York : North-Holland Pub. Co. ; Tokyo : Kodansha ; New York, NY : Sole distributors for the U.S.A. and Canada, Elsevier North-Holland, 1981.
Series: North-Holland mathematical library, v. 24.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Nobuyuki Ikeda; Shinzo Watanabe
ISBN: 0444861726 9780444861726
OCLC Number: 7277264
Description: xiv, 464 pages ; 23 cm.
Contents: Machine generated contents note: ch. I Preliminaries --
1.Basic notions and notations --
2.Probability measures on a metric space --
3.Expectations, conditional expectations and regular conditional probabilities --
4.Continuous stochastic processes --
5.Stochastic processes adapted to an increasing family of sub-fields --
6.Martingales --
7.Brownian motions --
8.Poisson random measure --
9.Point processes and Poisson point processes --
ch. II Stochastic integrals and Ito's formula --
1.Ito's definition of stochastic integrals --
2.Stochastic integrals with respect to martingales --
3.Stochastic integrals with respect to point processes --
4.Semi-martingales --
5.Ito's formula --
6.Martingale characterization of Brownian motions and Poisson point processes --
7.Representation theorem for semi-martingales --
ch. III Stochastic calculus --
1.The space of stochastic differentials --
2.Stochastic differential equations with respect to quasimartingales Note continued: 3.Moment inequalities for martingales --
4.Some applications of stochastic calculus to Brownian motions --
4.1.Brownian local time --
4.2.Reflecting Brownian motion and the Skorohod equation --
4.3.Excursions of Brownian motion --
4.4.Some limit theorems for occupation times of Brownian motion --
5.Exponential martingales --
6.Conformal martingales --
ch. IV Stochastic differential equations --
1.Definition of solutions --
2.Existence theorem --
3.Uniqueness theorem --
4.Solution by transformation of drift and by time change --
5.Diffusion processes --
6.Diffusion processes generated by differential operators and stochastic differential equations --
7.Stochastic differential equations with boundary conditions --
8.Examples --
9.Stochastic differential equations with respect to Poisson point processes --
ch. V Diffusion process on manifolds --
1.Stochastic differential equations on manifolds --
2.Flow of diffeomorphisms --
3.Heat equation on a manifold Note continued: 4.Non-degenerate diffusions on a manifold and their horizontal lifts --
5.Stochastic parallel displacement and heat equation for tensor fields --
6.The case with boundary conditions --
7.Kahler diffusions --
8.Malliavin's stochastic calculus of variation for Wiener functionals --
9.Pull-back of Schwartz distributions under Wiener mappings and the regularity of induced measures (probability laws) --
10.The case of stochastic differential equations: Applications to heat kernels --
ch. VI Theorems on comparison and approximation and their applications --
1.A comparison theorem for one-dimensional Ito processes --
2.An application to an optimal control problem --
3.Some results on one-dimensional diffusion processes --
4.Comparison theorem for one-dimensional projection of diffusion processes --
5.Applications to diffusions on Riemannian manifolds --
6.Stochastic line integrals along the paths of diffusion processes Note continued: 7.Approximation theorems for stochastic integrals and stochastic differential equations --
8.The support of diffusion processes --
9.Asymptotic evaluation of the diffusion measure for tubes around a smooth curve.
Series Title: North-Holland mathematical library, v. 24.
Responsibility: by Nobuyuki Ikeda and Shinzo Watanabe.

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