Ebook: Diffusion Processes and Related Problems in Analysis, Volume II: Stochastic Flows
- Tags: Probability Theory and Stochastic Processes, Partial Differential Equations, Applications of Mathematics
- Series: Progress in Probability 27
- Year: 1992
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
During the weekend of March 16-18, 1990 the University of North Carolina at Charlotte hosted a conference on the subject of stochastic flows, as part of a Special Activity Month in the Department of Mathematics. This conference was supported jointly by a National Science Foundation grant and by the University of North Carolina at Charlotte. Originally conceived as a regional conference for researchers in the Southeastern United States, the conference eventually drew participation from both coasts of the U. S. and from abroad. This broad-based par ticipation reflects a growing interest in the viewpoint of stochastic flows, particularly in probability theory and more generally in mathematics as a whole. While the theory of deterministic flows can be considered classical, the stochastic counterpart has only been developed in the past decade, through the efforts of Harris, Kunita, Elworthy, Baxendale and others. Much of this work was done in close connection with the theory of diffusion processes, where dynamical systems implicitly enter probability theory by means of stochastic differential equations. In this regard, the Charlotte conference served as a natural outgrowth of the Conference on Diffusion Processes, held at Northwestern University, Evanston Illinois in October 1989, the proceedings of which has now been published as Volume I of the current series. Due to this natural flow of ideas, and with the assistance and support of the Editorial Board, it was decided to organize the present two-volume effort.
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Stability and Equilibrium Properties of Stochastic Flows of Diffeomorphisms....Pages 3-35
Stochastic Flows on Riemannian Manifolds....Pages 37-72
Front Matter....Pages 73-73
Isotropic Stochastic Flows: A Survey....Pages 75-94
The Existence of Isometric Stochastic Flows for Riemannian Brownian Motions....Pages 95-109
Time Reversal of Solutions of Equations Driven by L?vy Processes....Pages 111-119
Birth and Death on a Flow....Pages 121-137
Front Matter....Pages 139-139
Lyapunov Exponents and Stochastic Flows of Linear and Affine Hereditary Systems....Pages 141-169
Convergence in Distribution of a Markov Process Generated by I.I.D. Random Matrices....Pages 171-200
Front Matter....Pages 201-201
Remarks on Ergodic Theory of Stochastic Flows and Control Flows....Pages 203-239
Stochastic bifurcation: instructive examples in dimension one....Pages 241-255
Lyapunov exponent and rotation number of the linear harmonic oscillator....Pages 257-267
The growth of energy of a free particle of small mass with multiplicative real noise....Pages 269-280
Front Matter....Pages 281-281
Iterated Function Systems and Multiplicative Ergodic Theory....Pages 283-305
Weak Convergence and Generalized Stability for Solutions to Random Dynamical Systems....Pages 307-314
Random Affine Iterated Function Systems: Mixing and Encoding....Pages 315-346
Back Matter....Pages 347-348
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Stability and Equilibrium Properties of Stochastic Flows of Diffeomorphisms....Pages 3-35
Stochastic Flows on Riemannian Manifolds....Pages 37-72
Front Matter....Pages 73-73
Isotropic Stochastic Flows: A Survey....Pages 75-94
The Existence of Isometric Stochastic Flows for Riemannian Brownian Motions....Pages 95-109
Time Reversal of Solutions of Equations Driven by L?vy Processes....Pages 111-119
Birth and Death on a Flow....Pages 121-137
Front Matter....Pages 139-139
Lyapunov Exponents and Stochastic Flows of Linear and Affine Hereditary Systems....Pages 141-169
Convergence in Distribution of a Markov Process Generated by I.I.D. Random Matrices....Pages 171-200
Front Matter....Pages 201-201
Remarks on Ergodic Theory of Stochastic Flows and Control Flows....Pages 203-239
Stochastic bifurcation: instructive examples in dimension one....Pages 241-255
Lyapunov exponent and rotation number of the linear harmonic oscillator....Pages 257-267
The growth of energy of a free particle of small mass with multiplicative real noise....Pages 269-280
Front Matter....Pages 281-281
Iterated Function Systems and Multiplicative Ergodic Theory....Pages 283-305
Weak Convergence and Generalized Stability for Solutions to Random Dynamical Systems....Pages 307-314
Random Affine Iterated Function Systems: Mixing and Encoding....Pages 315-346
Back Matter....Pages 347-348
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