The course is designed on advanced probability to cater to the needs of students and to the non-specialists. It would be suitable for research level courses in statistics. Uncertainties arises in several ways in different aspects of growth processes and also due to the  involvement of unpredictable human behavior, a brief description of stochastic processes and stochastic differential equation in terms of which different models have been incorporated.

After completion of the course, the students should

Understand the self-contained modules of concepts and notations.

Able to differentiate the deterministic and non-deterministic models.

Understand all features of stochastic epidemic processes and queue processes.

Develop maturity on stationary processes and time series.

At the end of the course, the students will be able to

Know when it is appropriate to use the properties of generating functions in different processes.

Know how the renewal theory and arguments have often been advanced in a variety of situations, such as demography, manpower studies, reliability, replacement and maintenance.

Create interest in the application of probability theory, concerned with objects or individuals that can generate objects of similar kinds, such as human beings, animals, genes, bacteria, and also neutrons which yield new neutrons under a nuclear chain.

Review of Stochastic Process and Markov Models: Definition, state space and parameters of stochastic process. Markov process, Markov Chain, Poisson Process, Birth and death process, Illness-Death Process, Branching process, Renewal Process and Queuing Process, Application of Markov Model and MCMC.

Stochastic Epidemic Process: The random variable technique and its application. Simple epidemic model, General epidemic model, Carrier borne epidemic model. Kermack and McKendrick’s model, Daley and Kendall’s Model. Stochastic Process of Clinical Drug Trials. Two armed bandit model, the Winner sampling model, the Optimum allocation model.

Models for Social and Occupational Mobility: Introduction, Models for social mobility, Models for occupational mobility.

Markov Models for Educational and Manpower Systems: A model for system with given Input. A model for an expanding system with given size.

Continuous Time Models for Stratified Social Systems: Some basic theory of Markov Processes. A manpower system with given Input. A  Manpower system with given growth rate. Systems with given Input and loss rate depending on length of service. Hierarchical systems with given input and promotion rates depending on seniority. Fix and Neyman Model.

Stochastic Models of Reproductive Process: Dandekar’s Modified binomial and Poisson model, Brass model, Singh’s modified model, Model of waiting times of conception Sheps and Perrin model of reproductive process.

Stochastic Process in Genetics:  Introduction, Physical basis of heredity. Genotypes under random mating, Herdy Weinberg law, Mating under various types of selection. Autosomal inheritance, Sex-linked inheritance, Change of gene frequencies, Homozygosity under random mating.

Stochastic Process in Queueing and Reliability: General concept, steady state and transient behavior of M/M/I models, Birth and death process, Multichannel  models, Network of Markovian queueing system, GI/M/I and M/G (a,b)/I Models.

1)

Bartholomew, D.J.(1973): Stochastic Models for Social Processes,  2nd ed. John Wiley and Sons.

2)

Biswas, S.(2004): Applied Stochastic Process, New Central Book Agency (P) Ltd., Kolkata, India.

3)

Medhi, J. (1994): Stochastic Process, Wiley Eastern Ltd., New Delhi, India.

4)

Anderson, T.W. (1971): The Statistical Analysis of Time Series, Wiley, N.Y

5)

Cryer, J. D. and K. Chan (2008): Time Series Analysis: with applications in R, 2nd Ed., Spinger, N.Y.

6(

Elandt Johnson, R.C.(1971): Probability Models and Statistical Methods in Genetics, John Wiley, N.Y.

7)

Lűtkepohl, H. (2005): New Introduction to multiple Time Series Analysis, Springer, N.Y.

8)

Tan Wai-Yuan(1991: Stochastic Process of Carcionogenesis, Marcel Dekker, N.Y.