Stochastic Process

Paper Code: 
STT 421
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

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 Outcomes: 

Students will able to

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

 

Paper Code

Paper Title

 STT 421

 

Stochastic Process

CO 94: Identify and formulate fundamental probability distribution and density functions, as well as functions of random variables.

 

CO 95: Explain the concepts of expectation and conditional expectation, and describe their properties.

 

CO 96: Analyze continuous and discrete-time random processes.

 

CO 97: Explain the concepts of stationary and wide-sense stationarity, and appreciate their significance.

 

CO 98: Formulate simple stochastic process models in the time domain and provide qualitative and quantitative analyses of such models.

 

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

 

15.00
Unit I: 

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.

 

15.00
Unit II: 

Canonical form 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.

 

 

15.00
Unit III: 

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.

 

15.00
Unit IV: 

Renewal process: renewal process when time is discrete and continuous. Renewal function and renewal density. Statements of Elementary renewal theorem and Key renewal theorem.

 

15.00
Unit V: 

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.

 

Essential Readings: 
  • Adke, S.R. & Manjunath 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

 

SUGGESTED READINGS:

  • 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.

 

e-RESOURCES:

 

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications
  • Stochastic Modeling and Applications, MUK Publications and Distributions

 

Academic Year: 
2023-2024
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