Introduction to Stochastic Integration

In the Leibniz–Newton calculus, one learns the differentiation and integration of deterministic functions. A basic theorem in differentiation is the chain rule, which gives the derivative of a composite of two differentiable functions. The chain rule, when written in an indefinite integral form, yields the method of substitution. In advanced calculus, the Riemann–Stieltjes integral is defined through the same procedure of “partition-evaluation-summation-limit” as in the Riemann integral. In...