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作者：Dalang, Robert C.; Mueller, Carl; Xiao, Yimin
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Rochester; Michigan State University
摘要：We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space-time white noise, or colored noise in spatial dimensions k >= 1. Our approach builds on a delicate covering argument developed by M. Talagrand [Ann. Probab. 23 (1995) 767-775; Probab. The...
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作者：Dalang, Robert C.; Humeau, Thomas
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We identify a necessary and sufficient condition for a Levy white noise to be a tempered distribution. More precisely, we show that if the Levy measure associated with this noise has a positive absolute moment, then the Levy white noise almost surely takes values in the space of tempered distributions. If the Levy measure does not have a positive absolute moment of any order, then the event on which the Levy white noise is a tempered distribution has probability zero.
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作者：Crepey, Stephane; Song, Shiqi
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：On a probability space (Omega, A, Q), we consider two filtrations F subset of G and a G stopping time theta such that the G predictable processes coincide with F predictable processes on (0,theta]. In this setup, it is well known that, for any F semimartingale X, the process X theta- (X stopped right before theta) is a G semimartingale. Given a positive constant T, we call theta an invariance time if there exists a probability measure P equivalent to Q on F-T such that, for any (F, P) local ma...
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作者：Bollobas, Bela; Duminil-Copin, Hugo; Morris, Robert; Smith, Paul
作者单位：University of Cambridge; University of Memphis; University of Geneva; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Tel Aviv University
摘要：The class of critical bootstrap percolation models in two dimensions was recently introduced by Bollobas, Smith and Uzzell, and the critical threshold for percolation was determined up to a constant factor for all such models by the authors of this paper. Here, we develop and refine the techniques introduced in that paper in order to determine a sharp threshold for the Duarte model. This resolves a question of Mountford from 1995, and is the first result of its type for a model with drift.
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作者：Jakubowski, Adam; Riedle, Markus
作者单位：Nicolaus Copernicus University; University of London; King's College London
摘要：A cylindrical Levy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Levy processes in Hilbert spaces. The space of admissible integrands consists of caglad, adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the int...
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作者：Kozma, Gady; Toth, Balint
作者单位：Weizmann Institute of Science; University of Bristol; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：We prove a central limit theorem under diffusive scaling for the displacement of a random walk on Z(d) in stationary and ergodic doubly stochastic random environment, under the H-1-condition imposed on the drift field. The condition is equivalent to assuming that the stream tensor of the drift field be stationary and square integrable. This improves the best existing result [Fluctuations in Markov Processes-Time Symmetry and Martingale Approximation (2012) Springer], where it is assumed that t...
