Lecture 24 (23/12/2021): Notes Video
Content: Absorption probabilities, gambler's ruin problem
Lecture 23 (20/12/2021): Notes Video
Content: For an aperiodic positive recurrent Markov chain, stationary distribution is the limiting distribution
Lecture 22 (16/12/2021): Notes Video
Content: Limiting distribution, existence of stationary distribution and irreducibility imply positive recurrence and hence uniqueness of stationary distribution
Lecture 21 (13/12/2021): Notes Video
Content: Proof of SLLN for positive recurrent Markov chains
Lecture 20 (09/12/2021): Notes Video
Content: Positive and null recurrence are class properties, computation of expected first return time for positive recurrent Markov chains, reversibility, statements of MCT, DCT and SLLN, introduction to SLLN for positive recurrent Markov chains
Lecture 19 (06/12/2021): Notes Video
Content: Invariant measure, existence and uniqueness of stationary distribution
Lecture 18 (02/12/2021): Notes Video
Content: Recurrent classes are closed, not all states in a finite state space Markov chain can be transient, introduction to stationary distribution
Lecture 17 (29/11/2021): Notes Video
Content: Transience of origin for simple random walk on Z^3, class properties, period of a state, canonical decomposition
Lecture 16 (25/11/2021): Notes Video
Content: Recurrence of origin for simple random walks on Z and Z^2
Lecture 15 (22/11/2021): Notes Video
Content: Characterization of transience (and recurrence) via summablility (and non-summability, resp.) of n-step transition probabilities
Lecture 14 (18/11/2021): Notes Video
Content: Dissection principle (the proof is just for your knowledge), introduction to recurrence, transience, positive recurrence and null recurrence
Lecture 13 (15/11/2021): Notes Video
Content: Communication classes, closed sets
Lecture 12 (11/11/2021): Notes Video
Content: Chapman-Kolmogorov equation, hitting time, accessibility of states
Lecture 11 (08/11/2021): Notes Video
Content: More examples of Markov chain, N-step transition probabilities
Lecture 10 (01/11/2021): Notes Video
Content: Definition and examples of Markov chain
Lecture 09 (28/10/2021): Notes Video
Content: Introduction to Markov chains
Practice Problems 1 (based on Lectures 1 - 8)
Lecture 08 (21/10/2021): Notes Video
Content: Superposition and thinning of homogeneous Poisson processes
Lecture 07 (18/10/2021): Notes Video
Content: Order statistics property and other properties of homogeneous Poisson processes
Lecture 06 (11/10/2021): Notes Video
Content: Completion of the proof of the characterization result for homogeneous Poisson processes, another manifestation of lack of memory property
Lecture 05 (07/10/2021): Notes Video
Content: A characterization of homogeneous Poisson processes and its proof (first part)
Lecture 04 (04/10/2021): Notes Video
Content: Independence and stationarity of increments of a homogeneous Poisson process
Lecture 03 (30/09/2021): Notes Video
Content: Properties of Poisson processes - manifestation of lack of memory property of exponential distribution
Lecture 02 (27/09/2021): Notes Video
Content: Definition of Poisson process as the number of arrivals
Lecture 01 (23/09/2021): Notes Video
Content: Introduction to homogeneous Poisson processes