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The Ornstein$-$Uhlenbeck process on $\mathscr P_2$ with a volatility operator
We analyze diffusion processes ${(μ_t)}_{t\geq 0}$ on the $2$-Wasserstein space $\mathscr P_2$ over $\mathbb R^d$, which can be classified as Ornstein--Uhlenbeck processes by means of their Fukushima decomposition. Characteristically for this class, $ | μ_t|_2^2-|μ_0|_2^2-2ct+2\int_0 ^t|μ_s|_2^2\,d
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