Interpolation (Levy-Ciesielski construction)
Cameron-Martin space eigenfunctions
White noise
Limit of Random walk
Hyperreals construction
see “A Non-standard Construction of Multi-Dimensional Brownian Motions and Option Pricing””.
Heat equation
The ![u(x,t)=E_{x}\left[g(B_{t})\chi\{t\leq \tau_{\Omega}\}\right]](https://s0.wp.com/latex.php?latex=u%28x%2Ct%29%3DE_%7Bx%7D%5Cleft%5Bg%28B_%7Bt%7D%29%5Cchi%5C%7Bt%5Cleq+%5Ctau_%7B%5COmega%7D%5C%7D%5Cright%5D&bg=ffffff&fg=333333&s=0&c=20201002)
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Tom Kojar website 