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...bolic integro-differential equations they play the same role that Brownian motion and more general diffusions play in the theory of second order parabolic eq ...of this process would look like the union of several disconnected Brownian motion paths. ...

...the unique solution $\mathbb{P}^{x}$ corresponds to the standard Brownian motion or Wiener process. Using this as a base case and using basic Ito Calculus o ...

...s start by an overview on how to derive the Laplace equation from Brownian motion. Let $B_t^x$ be Brownian motion starting at the point $x$ and $\tau$ be the first time it hits the boundary ...