= Stationary increments
A <stochastic process> has <Stationary increments> when the <probability distribution> of $X_{t+h}-X_t$ depends only on the duration $h$, whenever both times belong to the <index set>. The clock origin then does not change the <increment> law. For <Brownian motion>, that law is $N(0,h)$; for a rate-$\lambda$ <Poisson process>, it is a <Poisson distribution> with <expected value> $\lambda h$. Neither process itself is a <stationary process>: their <variances> grow with $t$. <Stationary increments> and a <stationary process> describe different properties.
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