Abstract
The following type of exponential convergence is proved for (non-degenerate or degenerate) McKean–Vlasov SDEs:
W2(μt , μ∞)2 + Ent(μt|μ∞) ≤ ce−λt min{W2(μ0 , μ∞)2, Ent(μ0|μ∞)}, t ≥ 1,
where c, λ > 0 are constants, μt is the distribution of the solution at time t, μ∞ is the unique invariant probability measure, Ent is the relative entropy and W2 is the L2-Wasserstein distance. In particular, this type of exponential convergence holds for some (non-degenerate or degenerate) granular media type equations generalizing those studied in Carrillo et al. (2003) and Guillin et al. (0000) on the exponential convergence in a mean field entropy.
W2(μt , μ∞)2 + Ent(μt|μ∞) ≤ ce−λt min{W2(μ0 , μ∞)2, Ent(μ0|μ∞)}, t ≥ 1,
where c, λ > 0 are constants, μt is the distribution of the solution at time t, μ∞ is the unique invariant probability measure, Ent is the relative entropy and W2 is the L2-Wasserstein distance. In particular, this type of exponential convergence holds for some (non-degenerate or degenerate) granular media type equations generalizing those studied in Carrillo et al. (2003) and Guillin et al. (0000) on the exponential convergence in a mean field entropy.
| Original language | English |
|---|---|
| Article number | 112259 |
| Journal | Nonlinear Analysis |
| Volume | 206 |
| Online published | 22 Jan 2021 |
| DOIs | |
| Publication status | Published - May 2021 |
Research Keywords
- Exponential convergence
- Granular media equation
- McKean–Vlasov SDE
- Stochastic Hamiltonian system