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.
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Paper Code |
Paper Title |
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STT 422(B) |
Stochastic Process (Theory)
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The students will be able to –
CO93: Identify and formulate fundamental probability distribution and density functions, as well as functions of random variables. CO94: Explain the concepts of expectation and conditional expectation, and describe their properties. CO95: Understand and analyze continuous and discrete-time random processes. CO96: Explain the concepts of stationary and wide-sense stationarity, and appreciate their significance.
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Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Field trips
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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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
- Adke, S.R. & Manju nath S.M. (1984) : An Introduction of Finite Markov Processes, Wiley Eastern.
- Bhatt ,B.R. (2000): Stochastic Models: Analysis and applications, New Age International, India
- Cox, P.R.(1970): Demography, Cambridge University Press
- Harris, T.E. (1963): The Theory of Branching processes, Springer-Verlag.
- Medhi, J (1982): Stochastic Processes, Wiley Eastern.
- Ballingsley, P (1962): Statistical Inference for Markov Chains, Chicago University Press, Chicago.
- Ross, S.M (1983): Stochastic Processes, Wiley.
