2026/07/23 by Renhai Wang, Zhang Chen, Bixiang Wang
#math.PR
The global-in-time well-posedness and uniform large deviation principles (LDPs) are investigated for a wide class of Mckean-Vlasov stochastic non-local fractional (α,p)-Laplacian equations with α∈ (0,1) and p>2 driven by superlinear multiplicative noise defined on the whole space ℝd, where the non-local nonlinear fractional (α,p)-Laplace operator is defined by a singular, symmetrical and translation invariant kernel function, the distribution-dependent drift terms have arbitrary polynomial growth and the distribution-dependent diffusion terms have superlinear growth. The global-in-time well-posedness is established under these conditions by using the monotone method and a domain expansion argument. Under additional conditions on the growth of diffusion terms, we establish the Freidlin-Wentzell and Dembo-Zeitouni uniform LDPs by using the generalized weak convergence method developed by Salins (Probab. Surv., 16:99-142, 2019). The idea of uniform tail-ends estimates, the pseudo monotone technique and the Arzelà-Ascoli theorem are combined to prove the weak-to-strong continuity of solution operators of the controlled equations in order to overcome many difficulties caused by the noncompactness of Sobolev embeddings on ℝd and the nonlinearity of the fractional (α,p)-Laplace operator. The superlinearly growing diffusion term is carefully controlled by using the dissipative drift terms and several algebraic inequalities.