STOCHASTIC MODELING AND APPLICATIONS

Course Objective: This course aims to give the students the basic concepts of stochastic modeling of linear and non-linear dynamic systems, their practical applications, and different approaches of stochastic systems analysis.

Syllabus:

Dynamic systems and their characteristics

-stochastic processes in dynamic systems-probability space-random variables-random processes-expectation-moments-characteristic functions-functional-canonic expansion-independent and conditional probabilities-

Random processes

-Brownian motion process-Gaussian process-Markov process-Wiener process-mean square calculus-second order process-Martingale

Stochastic integrals

-spectral and integral canonical representations- integral- differentials- stochastic calculus

General theory of stochastic systems and its applications

-methods of linear stochastic systems theory and applications-methods of general nonlinear stochastic systems theory and applications

References:

1. ‘Stochastic Systems – Theory and Applications’

–         V S Pugachev, I N Sinitsyn {Russian Academy of Sciences}

–         World Scientific Publishing, 2002

2. ‘Introduction to Stochastic Calculus with Applications’

–         Fima C Klabaner

–         Imperial College Press, 2001

3. ‘Probability, Random Variables, and Stochastic Process’

–         Papoulis Athanasios

–         2^nd Edition, McGraw-Hill, New York, 1984

4. ‘Applied Optimal Control & Estimation’

–         Frank L Lewis

–         Prentice-Hall, Englewood Cliffs, New Jersey , 1992

5. ‘Stochastic Models, Estimation, and Control’

–         Peter S Meybeck

–         Volume 1 & 2, Academic Press, New York, 1982

6. ‘Stochastic Process’

–         Parzen E

–         Holden Bay, San Francisco, 1962

7. ‘Introduction to Stochastic Control Theory’

–         Astrom K J

–         Academic Press, New York, 1970

Prerequisite: First level course in control systems and probability theory