Stochastic calculus extends classical differential and integral calculus to functions with random components. The fundamental construct in stochastic calculus is the Ito integral, a random variable that is a probabilistic extension of the Riemann integral. In this chapter we construct the integral, examine its properties, and describe its role in solving stochastic differential equations (SDEs).
11.1 Continuous-Time Stochastic Processes
Recall that a discrete-time stochastic process is a sequence of random variables on some probability space. As we have seen, such a construct is useful in modeling experiments consisting of a sequence of trials. However, while effective in many contexts, discrete-time models are ...
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