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."

One student, Sarah, frowned. "So how do we track it if the math breaks?" An Informal Introduction to Stochastic Calculus...

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 He turned back to the group, his eyes bright

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. "So how do we track it if the math breaks

"We change the rules," Leo grinned. "Enter . Imagine a drunkard’s walk in three dimensions. We can’t say where the glitter will be, but we can describe the distribution of where it might go. We stop looking for a single line and start looking at the 'drift' and the 'diffusion.'"

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."