Markov chains in discrete time. Poisson process. Birth and death process. Martingal in discreet time. Markov chains in continuous time. Brownian Movement. Martingal in continuous time. Integral of Itô. Itô formula. Stochastic Differential Equations. Representation of martingals. Measure change. Feynman-Kac formula.
- Hoel, P., Port, S. e Stone, C. (1986) Introduction to Stochastic Processes. Waveland.
- Steele , J. M. (2012). Stochastic Calculus and Financial Applications . Springer.
• Grimmett, G.R. and Stirzaker, D.R. (2001). Probability and random processes. Oxford.
• Oksendal, B. (2010). Stochastic differential equations: an introduction to applications. Springer. 6th Edition