Distribution dependence generally prevents McKean-Vlasov state solution maps from satisfying a cocycle identity, while the relevant Sobolev embedding is noncompact on unbounded domains. For a class of stochastic reaction-diffusion equations with a dissipative polynomial reaction, a one-sided monotone state-law coupling and finite-dimensional additive noise, we combine the deterministic law semiflow with the pathwise state evolution to construct a continuous random dynamical system on the product of the state space and its quadratic Wasserstein law space. An abstract product-space criterion, mixed-energy estimates, local regularity and uniform far-field estimates yield a unique pullback random attractor without global law contraction. Its law projection is the global attractor of the law semiflow, and its state fibers need not be singletons. Under an additional strict contraction condition, the law attractor reduces to the unique invariant law and the corresponding state fiber to a self-consistent random equilibrium. We also establish zero-noise upper semicontinuity and, in the contractive regime, quantitative convergence of the invariant laws and random equilibria with bounds linear in the noise amplitude.
We develop a quantitative framework for the long-time behavior of McKean--Vlasov stochastic differential equations with singular coefficients and possible phase transitions. The framework separates the existence of invariant measures from their uniqueness. For existence, we introduce a generalized Lyapunov condition wi...
We establish three weak averaging principles for distribution-dependent stochastic Navier--Stokes equations with rapidly oscillating coefficients on the torus $\T^2$. First, solution laws are relatively compact on finite time intervals, and every limit point as $\var\to0$ is the path law of a variational martingale sol...
Hong-Lei Chen, Z. M. I. O. S. Sciences, Dalian University of Technology· 0 citations
We study the long-term distributional dynamics and small-noise asymptotics of two-dimensional nonautonomous stochastic primitive equations driven by Gaussian and multiplicative L\'evy noise, together with moderate deviations for the purely jump model. For sufficiently small noise, uniform moment bounds and an exponenti...
We investigate the pathwise asymptotic dynamics of a nonlocal lattice equation with fixed delay on $\ell^2(\mathbb Z)$ driven by an infinite-dimensional stationary weakly geometric rough path. Using a rough-flow Doss-Sussmann transformation and the method of steps, we establish global well-posedness in the controlled-p...
We study a strongly damped stochastic wave equation on the three-dimensional torus driven by finite-rank pure-jump L\'{e}vy noise obtained from subordinated Brownian motion. Lyapunov estimates and an asymptotic compactness decomposition yield invariant measures, and a small-noise event gives weak irreducibility. To pro...
This paper studies a finite-horizon mixed $H_2/H_\infty$ feedback Nash game for stochastic evolution equations on a separable Hilbert space. The drift generator is unbounded, the remaining coefficients are bounded, and the one-dimensional Brownian diffusion depends on the state, control, and disturbance. The $H_2$ chan...
Ming-Yang Shen, Wei-Hai Zhang, Qing-Xin Meng et al.· 0 citations
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