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Stochastic Calculus

Code: MA688 | L-T-P-C: 3-0-0-6


Preamble / Objectives (Optional): This course aims to provide a mathematical introduction to the theory of stochastic calculus for continuous semi-martingales for students having some knowledge of measure theoretic probability. The main tool of stochastic calculus is Ito's formula and this course includes several important applications of Ito's formula and gives practice with explicit calculations. This course will also provide the necessary theoretical background for applications in other fields.

Course Content/Syllabus:Concepts from probability theory and stochastic processes, filtrations, martingales, Brownian motion. Continuous semi-martingales, existence of quadratic variation of a local martingale. Stochastic integration, construction of stochastic integral with respect to continuous semi-martingale. Ito's formula with applications: Levy's characterization of Brownian motion, continuous martingales as time changed Brownian motion, Burkholder-Davis-Gundy (BDG) inequalities, Girsanov's theorem with applications. Theory of Markov processes, Feller semi-groups.


  1. Jean-Francois Le Gall, Browninan Motion, Martingales, and Stochastic Calculus, Graduate Texts in Mathematics 274, Springer, 2016.
  2. F.C. Klebaner, Introduction to Stochastic Calculus with Applications, Imperial College Press, Third Edition, 2012.