Coming soon
Stochastic Process
This is a course on Stochastic Processes that aims at describing some advanced level topics in this area of research with a very strong potential of applications. This course also prepares students for undertaking research in this area. This also helps prepare students for applications of this important subject to agricultural sciences.
|
Course |
Learning outcomes (at course level |
Learning and teaching strategies |
Assessment Strategies
|
|
|---|---|---|---|---|
|
Paper Code |
Paper Title |
|||
|
STT- 422(B)
|
Stochastic Process |
CO 93: Identify and formulate fundamental probability distribution and density functions, as well as functions of random variables.
CO 94: Explain the concepts of expectation and conditional expectation, and describe their properties.
CO 95: Understand and analyze continuous and discrete-time random processes.
CO 96: Explain the concepts of stationary and wide-sense stationarity, and appreciate their significance.
|
Approach in teaching:
Interactive Lectures, Group Discussion, Classroom Assignment Problem Solving Sessions
Learning activities for the students:
Assignments Seminar Presentation Subject based Activities
|
Classroom Quiz Assignments Class Test Individual Presentation |
Introduction to stochastic process - classification according to state space and time domain. Finite and countable state Markov chains; time homogeneity; Chapman-Kolmogorov equations, marginal distribution and finite dimensional distributions. Classification of Markov chain.
Canonicalform of transition probability matrix of a Markov chain. Fundamental matrix; probabilities of absorption from transient states into recurrent classes in a finite Markov chain, mean time for absorption. Ergodic state and Ergodic chain. Stationary distribution of a Markov chain, existence and evaluation of stationary distribution. Random walk and gamblers ruin problem.
Discrete state continuous time Markov process: Kolmogorov difference – differential equations. Birth and death process, pure birth process (Yule- Fury process). Immigration-Emigration process. Linear growth process, pure death process.
Renewal process: renewal process when time is discrete and continuous. Renewal function and renewal density. Statements of Elementary renewal theorem and Key renewal theorem.
Branching process: Galton-Watson branching process. Mean and variance of size of nth generation, probability of ultimate extinction of a branching process. Fundamental theorem of branching process and applications. Introduction of Wiener process
1. Adke, S.R. & Manjunath S.M. (1984) : An Introduction of Finite Markov Processes, Wiley Eastern.
2. Bhatt ,B.R. (2000): Stochastic Models: Analysis and applications, New Age International, India
3. Cox,,P.R.(1970): Demography, Cambridge University Press
4. Harris, T.E. (1963): The Theory of Branching processes, Springer-Verlag.
5. Medhi, J (1982): Stochastic Processes, Wiley Eastern.
6. Ballingsley, P (1962) : Statistical Inference for Markov Chains, Chicago University Press, Chicago.
7. Ross, S.M (1983); Stochastic Processes, Wiley.
