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Brownian motion is the random motion of particles (eg atoms) that make up a gas. The math used to model Brownian motion is sometimes used in statistics to describe stochastic processes over time.

6 votes
1 answer
4k views

What's the intuition of variance, quadratic variation and total variation of Brownian Motion...

I'm familiar with the mathematic definitions of these three quantities, but having a hard time to really understand how to use them when actually dealing with discrete samples from a realization of a …
6 votes
1 answer
1k views

When is a stochastic process not differentiable?

Assume $\frac{dX_t}{X_t} = \mu dt + \sigma d B_t$ where $\mu$ is a constant and $B_t$ is a Brownian motion, and let $Y_t = \ln X_t$. I understand that $B_t$ is nowhere differentiable and both $X_t$ an …