As title says. Intuitively it seems clear it should be true from the definition of Wiener process since $\lambda t \ge 0$, i.e it should be the "same" process shifted $\lambda$ in time. But it doesn't feel a rigorous enough statement.
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1It's not the same process shifted by $\lambda$; it's the same process with time measured in different units (where the units-conversion is $\lambda$). If for the old process the units are weeks, and for the new one the units are days, then $\lambda = 7$. – John Hughes Dec 12 '15 at 15:31
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I see. Thanks for taking the time to answer. : ) – apelsimon Dec 12 '15 at 16:15