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作者：Fukasawa, Masaaki; Ugai, Takuto
作者单位：University of Osaka
摘要：Our study aims to specify the asymptotic error distribution in the dis-cretization of a stochastic Volterra equation with a fractional kernel. It is well known that for a standard stochastic differential equation, the discretization error, normalized with its rate of convergence 1/root n, converges in law to the solution of a certain linear equation. Similar to this, we show that a suitably normalized discretization error of the Volterra equation converges in law to the solution of a certain l...
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作者：Lehmkuehler, Matthis
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The family of SLE ⠂mu � 4 (-2) exploration processes with parameter mu e R forms a natural class of conformally invariant ways for discovering the loops of a conformal loop ensemble CLE4. Such an exploration consists of one simple continuous path called the trunk of the exploration that discovers CLE4 loops along the way. The parameter mu appears in the Loewner chain description of the path that traces the trunk and all CLE4 loops encountered by the trunk in chronological order. These explor...
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作者：Cuchiero, Christa; Rigger, Stefan; Svaluto-ferro, Sara
作者单位：University of Vienna; University of Verona
摘要：Supercooled Stefan problems describe the evolution of the boundary be-tween the solid and liquid phases of a substance, where the liquid is assumed to be cooled below its freezing point. Following the methodology of De-larue, Nadtochiy and Shkolnikov, we construct solutions to the one-phase one-dimensional supercooled Stefan problem through a certain McKean- Vlasov equation, which allows to define global solutions even in the presence of blow-ups. Solutions to the McKean-Vlasov equation arise ...
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作者：Rosenzweig, Matthew; Serfaty, Sylvia
作者单位：Massachusetts Institute of Technology (MIT); New York University
摘要：We consider the mean-field limit of systems of particles with singular interactions of the type -log |x| or |x|-s, with 0 < s < d - 2, and with an additive noise in dimensions d >= 3. We use a modulated-energy approach to prove a quantitative convergence rate to the solution of the corresponding limiting PDE. When s > 0, the convergence is global in time, and it is the first such result valid for both conservative and gradient flows in a singular setting on Rd. The proof relies on an adaptatio...
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作者：Kaushansky, Vadim; Reisinger, Christoph; Shkolnikov, Mykhaylo; Song, Zhuo Qun
作者单位：University of California System; University of California Los Angeles; University of Oxford; Princeton University; Princeton University; Princeton University
摘要：The supercooled Stefan problem and its variants describe the freezing of a supercooled liquid in physics, as well as the large system limits of sys-temic risk models in finance and of integrate-and-fire models in neuroscience. Adopting the physics terminology, the supercooled Stefan problem is known to feature a finite-time blow-up of the freezing rate for a wide range of initial temperature distributions in the liquid. Such a blow-up can result in a discon-tinuity of the liquid-solid boundary...
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作者：DEL Moral, Pierre; Horton, Emma; Jasra, Ajay
作者单位：Inria; King Abdullah University of Science & Technology
摘要：The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Fr...
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作者：Han, Qiyang; Jiang, Tiefeng; Shen, Yandi
作者单位：Rutgers University System; Rutgers University New Brunswick; University of Minnesota System; University of Minnesota Twin Cities; University of Chicago
摘要：Le Cam's third/contiguity lemma is a fundamental probabilistic tool to compute the limiting distribution of a given statistic T-n under a nonnull sequence of probability measures {Q(n)}, provided its limiting distribution under a null sequence {P-n} is available, and the log likelihood ratio {log(dQ(n)/dP(n))} has a distributional limit. Despite its wide-spread applications to low-dimensional statistical problems, the stringent requirement of Le Cam's third/contiguity lemma on the distribution...
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作者：Gheissari, Reza; Sinclair, Alistair
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：It is well known that Glauber dynamics on spin systems typically suffer exponential slowdowns at low temperatures. This is due to the emergence of multiple metastable phases in the state space, separated by narrow bottle-necks that are hard for the dynamics to cross. It is a folklore belief that if the dynamics is initialized from an appropriate random mixture of ground states, one for each phase, then convergence to the Gibbs distribution should be much faster. However, such phenomena have la...
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作者：Bonnier, Patric; Liu, Chong; Oberhauser, Harald
作者单位：University of Oxford; ShanghaiTech University
摘要：Two adapted stochastic processes can have similar laws but give different results in applications such as optimal stopping, queuing theory, or stochas-tic programming. The reason is that the topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. To address such discontinuities, Aldous introduced the extended weak topology, and subsequently, Hoover and Keisler showed that both, weak topology and ...
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作者：Tran, Hong Quan
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We consider the mean-field zero-range process in the regime where the potential function r is increasing to infinity at sublinear speed, and the den-sity of particles is bounded. We determine the mixing time of the system, and establish cutoff. We also prove that the Poincare constant is bounded away from zero and infinity. This mean-field estimate extends to arbitrary geome-tries via a comparison argument. Our proof uses the path-coupling method of Bubley and Dyer and stochastic calculus.
