Probabilistic Analysis and Related Topics

¿List of ContributorsPrefaceQualitative Theory of Stochastic Systems I. Introduction II. Scope of the Theory III. Nonlinear Systems IV. Linear Systems V. Linearization VI. Generalizations VII. Applications ReferencesLangevin Equations with Multiplicative Noise: Theory and Applications to Physical Processes I. Introduction II. Phase-Space Evolution: Cumulant Expansion Technique (Stratonovich) III. Phase-Space Evolution via Direct Integration (Itô and Stratonovich) IV. Examples ReferencesStability Theory of Stochastic Difference Systems I. Introduction II. Linear Stochastic Systems III. Stochastic Stability of Nonlinear Systems IV. Directions for Further Research ReferencesMarkov Properties for Random Fields Introduction I. Conditional Independence and Its Consequences II. Markov Properties for Multiparameter Processes III. Markov Property on a Class of Sets IV. Markov Properties for Generalized Random Fields V. Quasi-Invariant Measures and the Markov Property VI. Markov Property for Generalized Gaussian Random Fields VII. Markov Property for Solutions of Stochastic Partial Differential Equations Appendix A: Gaussian Processes and Reproducing Kernel Spaces Appendix B: Generalized Gaussian Random Field ReferencesThe Method of Random Contractors and Its Applications to Random Nonlinear Equations I. Introduction II. Contractors and Deterministic Nonlinear Operators III. Preliminary Definitions IV. Random Contractors and Application to Random Nonlinear Operator Equations V. Random Contractors with Random Nonlinear Majorant Functions VI. Random Step-Contractors VII. Integral Contractors and Applications to Random Equations ReferencesIndex