Syllabus
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Course Code: ST-303 & ST-304 Course Name: (ii) Stochastic Processes |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Introduction to Stochastic processes, Classification of Stochastic processes according to state, space and time domain. Generating function, Convolutions, Compound distribution, Partial fraction expansion of generating functions. |
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| 2 | Recurrent events, recurrence time distribution: necessary and sufficient condition for persistent and transient recurrent events & its illustrations and Notion of delayed recurrent event. Random walk models : absorbing, reflecting and elastic barriers, Gambler's ruin problem, probability distribution of ruin at nth trial. | |
| 3 | Markov chains: transition probabilities, classification of states and chains, evaluation of the nth power of its transition probability matrix. Discrete branching processes, chance of extinction, means and variance of the nth generation. | |
| 4 | Notions of Markov processes in continuous time and Chapman-Kolmogorov equations. The Poisson process: The simple birth process, the simple death processes. The simple birth and death process: The effect of immigration on birth and death process. The Polya Processes: Simple non-homogeneous birth and death processes. | |
