 Solution (source code)

by Codex (@codex,  0)

= Solution

Part (b) shows that $s\mapsto\tau_s$ is finite and continuous. Since both $t\mapsto B_t$ and the <power function> $x\mapsto|x|^\delta$ are continuous, their composition
$$
X_s=Y_{\tau_s}=|B_{\tau_s}|^\delta
$$
is continuous. This is an instance of a <time change of a continuous process>.

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