Abstract:We establish an integration by parts formula for the semigroup in time $T>0$ of the kinetic Brownian motion in the Euclidean plane together with its velocity in the circle. The stochastic differential equation of our kinetic Brownian motion is driven here by one real-valued Brownian motion constructed from an orthonormal basis of $L^2([0,T],\R)$ and an independent sequence of $\SN(0,1)$ random variables. Our method is based on an explicit computation of a Malliavin dual in the Gaussian space. We are mainly interested in large time $T$. From our integration by parts, we obtain gradient estimates including a reverse Poincar{é} inequality for the semigroup. As a direct consequence, we also obtain a Liouville property for the generator of the kinetic Brownian motion and its speed: all bounded harmonic functions are constant.
From: Magalie Benefice [view email] [via CCSD proxy]
[v1]
Wed, 18 Mar 2026 08:38:36 UTC (70 KB)
[v2]
Thu, 17 Sep 2026 08:56:58 UTC (74 KB)
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