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作者：Flandoli, Franco; Luo, Dejun
作者单位：Scuola Normale Superiore di Pisa; Chinese Academy of Sciences
摘要：We consider the vorticity form of the 2D Euler equations which is perturbed by a suitable transport type noise and has white noise initial condition. It is shown that stationary solutions of this equation converge to the unique stationary solution of the 2D Navier-Stokes equation driven by the space-time white noise.
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作者：Athreya, Siva; Butkovsky, Oleg; Mytnik, Leonid
作者单位：Indian Statistical Institute; Indian Statistical Institute Kolkata; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Technion Israel Institute of Technology
摘要：We consider the stochastic differential equation dX(t) = b(X-t) dt + dL(t), where the drift b is a generalized function and L is a symmetric one dimensional alpha-stable Levy processes, alpha is an element of (1, 2). We define the notion of solution to this equation and establish strong existence and uniqueness whenever b belongs to the Besov-Holder space C-beta for beta > 1/2 - alpha 1/2.
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作者：Hutzenthaler, Martin; Jentzen, Arnulf
作者单位：University of Duisburg Essen; University of Munster
摘要：We develop a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the L-p-distance between the solution process of an SDE and an arbitrary Ito process, which we view as a perturbation of the solution process of the SDE, by the L-q-distances of the differences of the local characteristics for suitable p, q > 0. As one application ...
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作者：Mousset, Frank; Noever, Andreas; Panagiotou, Konstantinos; Samotij, Wojciech
作者单位：Tel Aviv University; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Munich
摘要：Given a hypergraph Gamma = (Omega, chi) and a sequence p = (p(omega))(omega is an element of)(Q) of values in (0, 1), let Omega(p) be the random subset of Omega obtained by keeping every vertex omega independently with probability p(omega). We investigate the general question of deriving fine (asymptotic) estimates for the probability that Omega(p) is an independent set in Gamma, which is an omnipresent problem in probabilistic combinatorics. Our main result provides a sequence of upper and lo...
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作者：Campese, Simon; Nourdin, Ivan; Nualart, David
作者单位：University of Luxembourg; University of Kansas
摘要：Let Y = (Y(t))(t >= 0) be a zero-mean Gaussian stationary process with covariance function rho : R -> R satisfying rho (0) = 1. Let f : R -> R be a square-integrable function with respect to the standard Gaussian measure, and suppose the Hermite rank of f is d >= 1. If integral(R) vertical bar rho(s)vertical bar(d) ds < infinity, then the celebrated Breuer-Major theorem (in its continuous version) asserts that the finite-dimensional distributions of Z(epsilon) := root epsilon integral(./epsilo...
