... differential equations, and perhaps partial differential equations as well This is all too much to expect of undergrads But white noise, Brownian motion and the random calculus are wonderful topics, too ... trajectories of systems modeled by (ODE) not in fact behave as predicted: X(t) x0 Sample path of the stochastic differential equation Hence it seems reasonable to modify (ODE), somehow to include ... of these notes is to provide a rigorous interpretation for calculations like these, involving stochastic differentials Example According to Itˆ’s formula, the solution of the stochastic differential...