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Consider a continuous random walk $x (t) $, in which the velocity $v (t) = \mathrm dx/\mathrm dt $ rather than the position is described by Brownian motion, so that $v (t) = B_t $ where $B_{t+\epsilon}...

This's a wonderful book[1] but the latest edition I have is dated 1973. Is there recent book(s)/rewrite(s) that covers the same subjects and elucidate with more explicit arguments and details of their ...

I understand the concept of the 1 dimensional Brownian bridge with the form of: $$dx_t=\frac{-1}{1-t}x_t \, dt + dw_t$$ s.t. $x_0=0$ and $x_1=0$ where $dw_t$ is a Wiener process. I am thinking about ...