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فرآیندهای اتفاقی

To develop the subject of probability theory and stochastic processes as a deductive discipline and to illustrate the theory with basic applications of engineeling interest.

Deterministic and Stochastic Models, What is a Stochastic Process?,  Monte Carlo Simulation,  Conditional Probability,  Conditional Expectation, Markov Chain Cornucopia, Basic Computations, Long-Term Behavior—the Numerical Evidence,   Simulation, Mathematical Induction,  Limiting Distribution, Stationary Distribution, Can you Find the Way to State a?  Irreducible Markov Chains, Periodicity, Ergodic Markov Chains, Time Reversibility, Absorbing Chains, Regeneration and the Strong Markov Property,  Mean Generation Size, Probability Generating Functions,  Metropolis–Hastings Algorithm, Gibbs Sampler, Perfect Sampling, Rate of Convergence: the Eigenvalue Connection,  Card Shuffling and Total Variation Distance, Arrival, Interarrival Times, Infinitesimal Probabilities, Thinning, Superposition, Uniform Distribution,  Spatial Poisson Process,  Nonhomogeneous Poisson Process, Alarm Clocks and Transition Rates, Infinitesimal Generator,  Long-Term Behavior,  Time Reversibility,  Queueing Theory,  Poisson Subordination,  Brownian Motion and Random Walk, Gaussian Process, Transformations and Properties, Variations and Applications, Martingales,  Ito Integral, Stochastic Differential Equations.

References: 

ROBERT P. DOBROW, INTRODUCTION TO STOCHASTIC PROCESSES WITH R , John Wiley & Sons, 2016.

Athanasios Papoulis, PROBABILITY, RANDOM VARIABLES, AND STOCHASTIC PROCESSES, 4^th , ed., McGraw-Hill, 2002