Stochastic Processes (MT4254)  

Summary of all lectures

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• Lec.  01    05/01/2026  :  We had an interactive discussion about probabilistic aspects of snake and ladder game and their variations. We came across various notions like conditional probabilities, time homogeneity, average number of turns to win the game, fair/unfair dice that relate this example to Stochastic Processes in general. I also gave a short outline of the course contents in the end.

• Lec.  02     08/01/2026 : We defined some notions like filtration, stopping times, distributions about stochastic processes rigorously and saw more examples: Random walks, Poisson process in brief without all technical details. In the end we recalled the definition of conditional expectation. 

• Lec.  03     09/01/2026 :   We will study the Markov property, the definition and properties of Markov processes, Transition probability kernels. The non-random example of uniform motion was also discussed. We saw how the Random walk on integers satisfies the Markov property.

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Tentative plan for next few lectures:  

•  Lec.  04-06     12-16/01/2026 :  We will discuss more about probability kernels, Chapman-Kolmogorov equation. We will discuss the notion of sample paths and RCLL processes, We will define Markov chains, define transition probability matrix and semigroup of operators, and relate with Chapman-Kolmogorov equation, Stopping times and strong Markov property for discrete time Markov chains, Classification of states, Holding times, Stationary distributions and Limit theorems.