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I'm trying to prove that [tex]X=(X_{t})_{t\geq0}[/tex] is a Brownian Motion, where [tex]X_{t} = tB_{1/t}[/tex] for [tex]t\neq0[/tex] and [tex]X_{0} = 0[/tex]. I don't want to use the fact that it's a Gaussian process. So far I am stuck in proving:

[tex]\[

X_{t}-X_{s}=X_{t-s} \quad \forall \quad 0\leq s<t

\]

[/tex]

Anyone has any ideas?

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# Time inversion of Brownian motion

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