Stochastic Processes

I Introduction.- 1. Examples.- 2. Definitions.- 3. Classification according to the nature of E.- 4. Classification according to the nature of the set T of instants where the system is observed.- II Poisson processes.- A. Generalities - Point processes.- B. The uniform Poisson process.- C. Probability distributions associated to Poisson processes.- D. Extensions: Poisson-type-processes.- Problems for solution.- Random functions associated to a Poisson process.- III Numerical processes with independent random increments.- 1. Definition.- 2. Mean values - zero mean process.- 3. Variance distribution.- 4. Cumulants and second characteristic functions.- 5. Indicator function of a Poisson process.- 6. The Wiener-Levy process.- 7. Laplace processes with independent increments.- 8. General form of the random functions X (t) with independent increments.- 9. Infinitely divisible distributions.- 10. Stable distributions.- Problems for solution.- IV Markov processes.- A. Generalities and definitions.- B. Study by means of convexity.- C. Study by means of spectral analysis.- D. Direct algebraic study.- E. Reaching delays and sojourn duration problems.- F. Miscellaneous.- Problems for solution.- V Laplace processes and second order processes.- 1. Introduction.- A. Second order properties.- B. Laplace processes.- Problems for solution.- VI Some Markov processes on continuous-time.- 1. Homogeneous Laplace-Markov sequences.- 2. Stationary Laplace-Markov sequence.- 3. Estimation problems.- 4. Interpolation - permanent process.- 5. Non homogeneous standardized Laplace-Markov processes.- 6. General form of Laplace-Markov processes.- 7. Wiener-Levy processes.- 8. Poisson-Markov processes.- Problems for solution.- Answers to problems.