Format:
Online-Ressource
ISBN:
9783642110795
Series Statement:
C.I.M.E. Summer Schools 77
Content:
C. Doleans-Dade: Stochastic processes and stochastic differential equations.- A. Friedman: Stochastic differential equations and applications.- D.W. Stroock, S.R.S. Varadhan: Theory of diffusion processes.- G.C. Papanicolaou: Wave propagation and heat conduction in a random medium.- C. Dewitt Morette: A stochastic problem in Physics.- G.S. Goodman: The embedding problem for stochastic matrices
Note:
Description based upon print version of record
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Stochastic Differential Equations; Copyright Page; Contents; Stochastic Processes and Stochastic Differential Equations; Introduction; Stopping Times and Stochastic Processes; Stopping Times; Stochastic Processes; Chapter II: Martingales, Local Martingales and Semimartingales; Chapter III: Why Semimartingales?; Chapter IV: More on Local Martingales and Semimartingales; Chapter V: Stochastic Integrals; Chapter VI: ITO's Formula; Chapter VII: Stochastic Differential Equations; Bibliography; Stochastic Differential Equations and Applications; 1. Brownian motion; 2. The stochastic integral
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3. Ito's formula4. Stochastic differential equations; 5. Probabilistic interpretation of boundary value problems; 6. Stopping time problems and variational inequalities; 7. Stochastic switching and nonlinear elliptic equations; 8. Probabilistic methods in singular perturbations; References; Theory of Diffusion Processes; Section I; Section II; Section III; Section IV; Wave Propagation and Heat Conduction in a Random Medium; Introduction; 1. Formulation of the Problems; 2. Limit Theorems for Stochastic Equations; 3. Application to the Transmission Coefficient
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4. Application to the Heat Conduction Problem5. Proof of a Limit Theorem; 6. The Instability of the Harmonic Oscillator; References; A Stochastic Problem in Physics; Introduction; Appendix; References; The Embedding Problem for Stochastic Matrices; 1. Statement of the embedding problem; 2. The Kolmogorov Equations; 3. Control-theoretic; 4. properties of the reachable set; 5. The bang-bang conjecture; 6. The determinantal inequality; 7. Geometrical representation of stochastic matrices; 8. A pre-order for stochastic matrices; 9. A geometric formulation of the embedding problem
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10. Bang-bang controls in the restricted embedding problem11. A characterization of the reachable set; 12. Recent work and the bang-bang conjecture; Note added August 10, 1978; References;
Language:
English
Keywords:
Electronic books
