Sticky couplings of multidimensional diffusions with different drifts. (English. French summary) Zbl 1434.60213
Summary: We present a novel approach of coupling two multi-dimensional and non-degenerate Itô processes \((X_t)\) and \((Y_t)\) which follow dynamics with different drifts. Our coupling is sticky in the sense that there is a stochastic process \((r_t)\), which solves a one-dimensional stochastic differential equation with a sticky boundary behavior at zero, such that almost surely \(|X_t-Y_t|\leq r_t\) for all \(t\geq0\). The coupling is constructed as a weak limit of Markovian couplings. We provide explicit, non-asymptotic and long-time stable bounds for the probability of the event \(\{X_t=Y_t\} \).
MSC:
| 60J60 | Diffusion processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
diffusion process; reflection coupling; sticky boundary conditions; stochastic stability; perturbations of Markov processes; total variation bounds; McKean-VlasovReferences:
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