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Sharp variational, jump and oscillation bounds in a general Gaussian context
We consider a general, nonsymmetric Ornstein--Uhlenbeck semigroup $(\mathcal H_t)_{t>0}$. We prove an $L^p$ bound for the jump quasi-seminorms for $1 < p < \infty$ and a weak type (1,1) oscillation inequality, both with respect to the invariant measure. These results are established for the order $\
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