Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations

McKean-Vlasov SDEs and SPDEs with Locally Monotone Coefficients

“…The well-posedness and LDP result for distribution dependent stochastic porous media equation have been established in the recent works [28,29,30], however, under our new framework constructed in Section 3.1, one can easily extend the results of [28,29,30] to more general cases. Remark 6.2 We remark that Theorems 3.1 and 4.1 can be used to obtain the well-posedness and LDP directly for the distribution dependent stochastic p-Laplace equations (p > 1), see [47,Example 4.1.9].…”

“…(ii) Compared to the existing works [15,30,49] on the LDP for the distribution dependent SDE/SPDEs, the result of Theorem 4.1 is even new in the finite-dimensional case (i.e. V = H = V * = R d ).…”

“…Afterwards, Adams et al [1] extended the results of [15] to the case of reflected distribution dependent SDEs with self-stabilising terms. By employing the weak convergence approach, Liu et al [49] investigated the LDP and moderate deviation principle for distribution dependent SDEs under a similar framework as [15] but with Lévy noise, see also [30] for the extension to the infinite dimensional case. Inspired by [1,15,30,49,63], one natural question is whether the Freidlin-Wentzell type LDP holds for distribution dependent equations under fully local assumptions?…”

“…[44,48,55,71]) and also for distribution dependent S(P)DEs (cf. [1,15,30,49,63]). As a consequence, we can directly obtain the LDP for a large class of distribution dependent SPDE models.…”

Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions

“…Another general approach for studying large and moderate deviation problems is the well-known weak convergence method introduced in [7,10], which is based on a variational representation for positive functionals of Brownian motion or Poisson random measure. After that, this approach has been wildly applied in various stochastic dynamical systems, see, for example, [5,9,11,17,18,19,23,27,31,42,45,47] and the references therein. In the study of moderate deviation principle (MDP), one is concerned with deviation probability of a lower order than that in large deviation principle (LDP), which actually bridges the gap between LDP and central limit theorem (CLT) (see more details in the next paragraph).…”