A Coupling Approach¶to Randomly Forced Nonlinear PDE's. I

By Sergei B. Kuksin, Armen Shirikyan. 2001

148 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/027111141ad87f80ba447f92e68a7343b2763149

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Citations in the corpus

Spectral gaps in Wasserstein distances and the 2D stochastic Navier–Stokes equations (2006, background): “Until recently, the consensus that emerged in [5, 6, 14, 20, 28, 34, 37, 38] was that the uniqueness of the invariant measure can be obtained, provided that all the qk with |k|2 ≤ N are nonzero, for some value N ≈ ∑q2 k /ν3.”
Ergodic Theory of Infinite Dimensional Systems¶with Applications to Dissipative Parabolic PDEs (2002, unknown): “3.3 and 4.3.”
Strong and weak orders in averaging for SPDEs (2012, methodology): “This technique was first used in the study of the asymptotic behaviour of Markov chains – see [1,8,14,17] – and was later adapted for SDEs and more recently for SPDEs—see for instance [13,16].”
Exponential ergodicity for stochastic Burgers and 2D Navier–Stokes equations (2005, unknown): “[21].”
Coupling approach to white-forced nonlinear PDEs (2002, background): “ KPS02 , Kuk02] applies to the white-forced NS system.”
Exponential ergodicity and regularity for equations with Lévy noise (2011, background): “We refer the reader to [13,19,35] for discrete-time random perturbations, to [21,11,14,36,24] for a white noise, to [22] for a compound Poisson process, and to the book [15] for further references on this subject.”
2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term (2008, background): “Recently much progress has been obtained in the study of existence, uniqueness and ergodicity of the associated invariant measures ([3], [15], [17], [18], [19], [20], [ 21 ], [11], [22], [23]) when f(t) = 0. Also in the 3D case, there has been a lot of recent progress ([6], [9], [13], [16], [25], [2”
Ergodicity of stochastic differential equations driven by fractional Brownian motion (2003, methodology): “We refer to [Mat02, KS01 , Hai02] for implementations of this idea in the Markovian case.”