Stochastic Differential Equations: With Applications to Physics and Engineering [Paperback]

Introduction: Origin of Stochastic Differential Equations.- I. Stochastic Processes  Short Resum?.- 1. Introductory Remarks.- 2. Probability and Random Variables.- 2.1. Basic concepts.- 2.2. Some probability distributions.- 2.3. Convergence of sequences of random variables.- 2.4. Entropy and information of random variables.- 3. Stochastic Processes  Basic Concepts.- 4. Gaussian Processes.- 5. Stationary Processes.- 6. Markov Processes.- 6.1. Basic definitions.- 6.2. Diffusion processes.- 6.3. Methods of solving the Kolmogorov equation.- 6.4. Vector diffusion processes.- 7. Processes With Independent Increments; Wiener Process And Poisson Process.- 7.1. Definition and general properties.- 7.2. Wiener process.- 7.3. Poisson process.- 7.4. Processes related to Poisson process.- 8. Point Stochastic Processes.- 9. Martingales.- 10. Generalized Stochastic Processes; White Noise.- 11. Processes with Values in Hilbert Space.- 12. Stochastic Operators.- Examples.- II. Stochastic Calculus: Principles and Results.- 13. Introductory Remarks.- 14. Processes of Second Order; Mean Square Analysis.- 14.1. Preliminaries.- 14.2. Mean-square continuity.- 14.3. Mean-square differentiation.- 14.4. Mean-square stochastic integrals.- 14.5. Orthogonal expansions.- 14.6. Transformations of second-order stochastic processes.- 14.7. Mean-square ergodicity.- 15. Analytical Properties of Sample Functions.- 15.1. Sample function integration.- 15.2. Sample function continuity.- 15.3. Sample function differentiation.- 15.4. Relation to second-order properties.- 16. IT? Stochastic Integral.- 17. Stochastic Differentials. IT? Formula.- 18. Counting Stochastic Integral.- 19. Generalizations.- Examples.- III. Stochastic Differential Equations: Basic Theory.- 20. Introductory Remarks.- 21. Regular Stochastic Differential Equations.- 21.1. Mean-square theory.- 21.2. Sample function solutions.- 21.3. Analysis via stochastic operators.- 21.4. Asymptotic analysis.- 21.5. Stationary solutions.- 22. IT? StlĂ`