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Prove the reflected Brownian motion of a Wiener process is a Markov process.

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Let Wt be a standard Wiener process and define the reflected Brownian motion as Z(t) = |W(t)|. Show that the reflected Brownian motion is a Markov process and express its transition probability density function
p(t; x, y) in terms of the transition density

of the standard Wiener process
Hint: Prove that the following identity holds for all times 0 < t1 < ...<tn
and s > 0
P(Z(tn+s) < z |Z(t0) = z0, ..., Z(tn) = zn) =

And deduce the result from this.

Please see the attached file for the fully formatted problems.
keywords: weiner

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It is proven that the reflected Brownian motion of a Wiener process is a Markov process. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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