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作者：Aistleitner, Christoph; Fukuyama, Katusi
作者单位：Graz University of Technology; Kobe University
摘要：Let (n(k)) k >= 1 be an increasing sequence of positive integers. Bobkov and Gotze proved that if the distribution of cos 2 pi n(1)x + ... + cos 2 pi nNx/root N converges to a Gaussian distribution, then the value of the variance is bounded from above by 1/2 - lim sup k/(2n(k)). In particular it is impossible that for a sequence (n(k)) k >= 1 with bounded gaps (i.e. n(k+1) - n(k) <= c for some constant c) the distribution of (1) converges to a Gaussian distribution with variance sigma(2) = 1/2...
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作者：Conus, Daniel; Khoshnevisan, Davar
作者单位：Utah System of Higher Education; University of Utah
摘要：We study the stochastic heat equation partial derivative(t)u = Lu + sigma(u)(W) over dot in (1 + 1) dimensions, where (W) over dot is space-time white noice sigma : R -> R is Lipschitz continuous, and L is the generator of a symmetric L,vy process that has finite exponential moments, and u (0) has exponential decay at +/- a. We prove that under natural conditions on sigma : (i) The nu th absolute moment of the solution to our stochastic heat equation grows exponentially with time; and (ii) The...
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作者：Mijatovic, Aleksandar; Urusov, Mikhail
作者单位：Ulm University; University of Warwick
摘要：The stochastic exponential Z(t) = exp{M-t - M-0 - (1/2) < M, M >(t)} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the process Z to be a true martingale in the case where M-t = integral(t)(0)b(Yu) dW(u) and Y is a one-dimensional diffusion driven by a Brownian motion W. Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting. These conditions are...
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作者：Mikulevicius, R.; Rozovskii, B. L.
作者单位：Brown University; University of Southern California
摘要：A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the original nonlinear term . This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The perturbed equation is solved in the space of generalized stochastic processes usin...
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作者：Du, Kai; Tang, Shanjian
作者单位：Fudan University; Fudan University; Ajou University
摘要：This paper is concerned with the strong solution to the Cauchy-Dirichlet problem for backward stochastic partial differential equations of parabolic type. Existence and uniqueness theorems are obtained, due to an application of the continuation method under fairly weak conditions on variable coefficients and C (2) domains. The problem is also considered in weighted Sobolev spaces which allow the derivatives of the solutions to blow up near the boundary. As applications, a comparison theorem is...
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作者：Chatterjee, Sourav
作者单位：New York University
摘要：We revisit strong approximation theory from a new perspective, culminating in a proof of the Komls-Major-Tusnady embedding theorem for the simple random walk. The proof is almost entirely based on a series of soft arguments and easy inequalities. The new technique, inspired by Stein's method of normal approximation, is applicable to any setting where Stein's method works. In particular, one can hope to take it beyond sums of independent random variables.
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作者：Beffara, Vincent; Duminil-Copin, Hugo
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); University of Geneva
摘要：We prove a long-standing conjecture on random-cluster models, namely that the critical point for such models with parameter q a parts per thousand yen 1 on the square lattice is equal to the self-dual point . This gives a proof that the critical temperature of the q-state Potts model is equal to for all q a parts per thousand yen 2. We further prove that the transition is sharp, meaning that there is exponential decay of correlations in the sub-critical phase. The techniques of this paper are ...
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作者：Osada, Hirofumi
作者单位：Kyushu University
摘要：We solve infinite-dimensional stochastic differential equations (ISDEs) describing an infinite number of Brownian particles interacting via two-dimensional Coulomb potentials. The equilibrium states of the associated unlabeled stochastic dynamics are the Ginibre random point field and Dyson's measures, which appear in random matrix theory. To solve the ISDEs we establish an integration by parts formula for these measures. Because the long-range effect of two-dimensional Coulomb potentials is q...
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作者：Fleming, Benjamin J.; Forrester, Peter J.; Nordenstam, Eric
作者单位：Royal Institute of Technology; University of Melbourne
摘要：The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an abc-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random m...
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作者：Hansen, Wolfhard
作者单位：University of Bielefeld
摘要：The 3G-inequality for Green functions g(D) on arbitrary bounded domains in R-2, which Bass and Burdzy (Probab Theory Relat Fields 101(4): 479- 493, 1995) obtained by a genuinely probabilistic proof (using loops of Brownian motion around the origin), is proven (in a more precise form) employing elementary properties of harmonic measures only. Since harmonic measures are hitting distributions of Brownian motion, this purely analytic proof can be viewed as well as being probabilistic. A spin- off...
