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作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; Sorbonne Universite; Universite Paris Cite
摘要：Tick-by-tick asset price data exhibit a number of empirical regularities, including discreteness, long periods where prices are flat, periods of price moves of alternating plus and minus one tick, periods of rapid successive price moves of the same sign, and others. This paper proposes a framework to examine whether and how these microscopic features of the tick data are compatible with the typical macroscopic continuous-time models, based on Ito semimartingales, that are employed to represent...
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作者：Horton, Emma; Kyprianou, Andreas E.; Villemonais, Denis
作者单位：Universite de Lorraine; University of Bath
摘要：The neutron transport equation (NTE) describes the flux of neutrons through an inhomogeneous fissile medium. In this paper, we reconnect the NTE to the physical model of the spatial Markov branching process which describes the process of nuclear fission, transport, scattering, and absorption. By reformulating the NTE in its mild form and identifying its solution as an expectation semigroup, we use modern techniques to develop a Perron-Frobenius (PF) type decomposition, showing that growth is d...
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作者：Bayraktar, Erhan; Ekren, Ibrahim; Zhang, Yili
作者单位：University of Michigan System; University of Michigan; State University System of Florida; Florida State University
摘要：For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin, Peres and Sivan (In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (2016) 528-547, ACM), the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts.
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作者：Bazhba, Mihail; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
作者单位：Stanford University; Northwestern University
摘要：We study sample path large deviations for Levy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. The sharpness and applicability of these results are illustrated by a counterexample proving the nonexistence of a full LDP in the J(1) topology, and by an application to a first passage problem.
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作者：Breit, Dominic; Feireisl, Eduard; Hofmanova, Martina
作者单位：Heriot Watt University; Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; University of Bielefeld
摘要：We analyze the Markov property of solutions to the compressible Navier-Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem. Our proof is based on the abstract framework introduced in Flandoli and Romito (Probab. Theory Related Fields 40 (2008) 407-458). A major difficulty arises from the fact, different from the incompressible case, that the velocity field is not continuous in time...
