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In Wikipedia a formula is given for the distribution of $$M_t = \max_{0\leq s \leq t} W_s$$ even conditioned on $W_t$.

I wonder if there is also a simple expression for (note the absolute value) $$\tilde M_t = \max_{0\leq s \leq t} |W_s|$$ maybe conditioned on $|W_t|$?

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the derivation of $M_t$ comes from reflection principle. At moment, i cannot see how it would work for $\tilde{M}$ –  Lost1 Apr 10 '13 at 9:32

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