He pulled a small notebook from his pocket. "The hero of our story is . In normal calculus, the change in a function depends on the change in
Professor Leo Thorne didn’t believe in lecturing from a podium. Instead, he led his graduate students to the edge of the campus fountain, a chaotic splash of water catching the afternoon light. An Informal Introduction to Stochastic Calculus...
He turned back to the group, his eyes bright. "Now, let’s go inside and see why dt2d t squared equals zero, but dW2d cap W squared . That’s where the magic starts." He pulled a small notebook from his pocket
He pointed to a single fleck of gold dancing violently atop the ripples. "That is a . It’s being buffeted by a billion microscopic collisions every second. It’s not moving along a smooth curve; it’s jittering. If you try to take a standard derivative of that path, you’ll fail. The path is continuous, but it’s nowhere differentiable. It’s too 'spiky' for Newton." Instead, he led his graduate students to the