Introduction to Stochastic Integration

It was the beginning of the Itˆ o calculus, the counterpart of the Leibniz–Newton calculus for random functions. The Itˆ o formula is the chain rule for the Itˆocalculus.Butitcannotbe expressed as in the Leibniz–Newton calculus in terms of derivatives, since a Brownian motion path is nowhere di?erentiable.