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作者：Roeckner, Michael; Zhu, Rongchan; Zhu, Xiangchan
作者单位：University of Bielefeld; Beijing Institute of Technology; Beijing Jiaotong University
摘要：In this paper, we study the 2D stochastic quasi-geostrophic equation on T-2 for general parameter alpha epsilon (0, 1) and multiplicative noise. We prove the existence of weak solutions and Markov selections for multiplicative noise for all alpha epsilon (0, 1). In the subcritical case alpha > 1/2, we prove existence and uniqueness of (probabilistically) strong solutions. Moreover, we prove ergodicity for the solution of the stochastic quasi-geostrophic equations in the subcritical case driven...
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作者：Lawler, Gregory F.; Rezaei, Mohammad A.
作者单位：University of Chicago
摘要：We prove the existence and nontriviality of the d-dimensional 4 Minkowski content for the Schramm-Loewner evolution (SLE kappa) with kappa < 8 and d = 1 + kappa/8 We show that this is a multiple of the natural parameterization.
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作者：Norris, James; Turner, Amanda
作者单位：University of Cambridge; Lancaster University
摘要：We define a new state-space for the coalescing Brownian flow, also known as the Brownian web, on the circle. The elements of this space are families of order-preserving maps of the circle, depending continuously on two time parameters and having a certain weak flow property. The space is equipped with a complete separable metric. A larger state-space, allowing jumps in time, is also introduced, and equipped with a Skorokhod-type metric, also complete and separable. We prove that the coalescing...
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作者：Brofferio, Sara; Buraczewski, Dariusz
作者单位：Universite Paris Saclay; Universite Paris Saclay; University of Wroclaw
摘要：We consider stochastic dynamical systems on R, that is, random processes defined by X-n(x) = Psi(n)(X-n-1(x)), X-0(x) = x, where Psi(n) are i.i.d. random continuous transformations of some unbounded closed subset of R. We assume here that Psi(n) behaves asymptotically like A(n)x, for some random positive number A(n) [the main example is the affine stochastic recursion Psi(n) (x) = A(n)x + B-n]. Our aim is to describe invariant Radon measures of the process X-n(x) in the critical case, when E l...
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作者：Dupuis, Paul; Liu, Yufei
作者单位：Brown University; Alphabet Inc.; Google Incorporated
摘要：The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a variational problem, and in this sense not explicit. An interesting class of continuous time, reversible processes was identified in the original work of Donsker and Varadhan for which an explicit expression is possible. While this class includes many (revers...
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作者：Foss, Sergey; Rolla, Leonardo T.; Sidoravicius, Vladas
作者单位：Heriot Watt University; University of Buenos Aires
摘要：We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space time half plane. The server adopts a greedy routing mechanism, traveling toward the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.
