Stochastic Integration

A tremendous range of problems in the natural, social, and biological sciences came under the dominion of the theory of functions of a real variable when Newton and Leibniz invented the calculus. The primary components of this invention were the use of differentiation to describe rates of change, the use of integration to pass to the limit in approximating sums, and the fundamental theorem of calculus, which relates the two concepts and thereby makes the latter amenable to computation. All of this gave rise to the concept of ordinary differential equations, and it is the application of these equations to the modeling of real-world phenomena which reveals much of the power of calculus.