This is an introductory course in stochastic processes. The course places emphasis on "probabilistic thinking and " and on learning how to model the real-life phenomena, which evolve over time. It presents classes of stochastic processes which are widely used as modeling tools in diverse fields of applications including finance, economics, accounting, marketing and actuarial science. It covers basic theory and applications of discrete and continuous- time Markov chains; discrete and continuous time martingales; and Brownian motion and its generalizations. The introduction to Ito stochastic calculus is presented with a view towards financial applications. The course also discusses some statistical aspects of considered processes.
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