= Continuous Lévy process
{title2=$X_t=bt+\sigma W_t$}
A real <Lévy process> with <continuous function>[continuous paths] is <Brownian motion> with deterministic linear drift: $X_t=bt+\sigma W_t$. <continuity> forces the jump measure in the <Lévy–Khintchine formula> to vanish, leaving <Characteristic function> $\exp(t(ibu-\sigma^2u^2/2))$. If its law is also invariant under $X_t\mapsto\lambda^{-1}X_{\lambda^2t}$ for every $\lambda>0$, then $b=0$. The zero-variance case is included.
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