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作者：Lionnet, Arnaud; dos Reis, Goncalo; Szpruch, Lukasz
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; University of Edinburgh
摘要：The theory of Forward-Backward Stochastic Differential Equations (FBSDEs) paves a way to probabilistic numerical methods for nonlinear parabolic PDEs. The majority of the results on the numerical methods for FBSDEs relies on the global Lipschitz assumption, which is not satisfied for a number of important cases such as the Fisher-KPP or the FitzHugh- Nagumo equations. Furthermore, it has been shown in [Ann. Appl. Probab. 25 (2015) 2563-2625] that for BSDEs with monotone drivers having polynomi...
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作者：Cuchiero, Christa; Larsson, Martin; Svaluto-Ferro, Sara
作者单位：University of Vienna; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit simplex under natural structural hypotheses on the jumps. As a stepping stone, we characterize well-posedness of the martingale problem for polynomial operators on general compact state spaces.
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作者：Jagannath, Aukosh; Ko, Justin; Sen, Subhabrata
作者单位：University of Toronto; Stanford University
摘要：We study the asymptotic behavior of the Max kappa-cut on a family of sparse, inhomogeneous random graphs. In the large degree limit, the leading term is a variational problem, involving the ground state of a constrained inhomogeneous Potts spin glass. We derive a Parisi-type formula for the free energy of this model, with possible constraints on the proportions, and derive the limiting ground state energy by a suitable zero temperature limit.
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作者：Touboul, Jonathan
作者单位：Institut National de la Sante et de la Recherche Medicale (Inserm); Universite PSL; College de France
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作者：Schumacher, Christoph; Schwarzenberger, Fabian; Veselic, Ivan
作者单位：Dortmund University of Technology
摘要：We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone and almost additive, with finite range dependence. Using the theory of quasi-tilings we prove an uniform ergodic theorem, more precisely, that averages along a Folner sequence converge uniformly to a limiting function. Moreover, we give explicit error estimates for the ...
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作者：Pitman, Jim; Yakubovich, Yuri
作者单位：University of California System; University of California Berkeley; Saint Petersburg State University; Saint Petersburg State University
摘要：We describe the distribution of frequencies ordered by sample values in a random sample of size n from the two parameter GEM(alpha, theta) random discrete distribution on the positive integers. These frequencies are a (size-alpha)-biased random permutation of the sample frequencies in either ranked order, or in the order of appearance of values in the sampling process. This generalizes a well-known identity in distribution due to Donnelly and Tavare [Adv. in Appl. Probab.18 (1986) 1-19] for al...
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作者：Guo, Heng; Jerrum, Mark
作者单位：University of Edinburgh; University of London; Queen Mary University London
摘要：We show that the mixing time of Glauber (single edge update) dynamics for the random cluster model at q = 2 on an arbitrary n-vertex graph is bounded by a polynomial in n. As a consequence, the Swendsen Wang algorithm for the ferromagnetic Ising model at any temperature also has a polynomial mixing time bound.
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作者：Qian, Zhongmin; Xu, Mingyu
作者单位：University of Oxford; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：In this article, we study a class of reflected backward stochastic differential equations (introduced in El Karoui et al. [Ann. Probab. 25 (1997) 702-737], RBSDE for short) with nonlinear resistance by means of Skorohod's equation. The advantage of this approach lies in its pathwise nature and, therefore, provides additional information about solutions of RBSDE. As an application of our approach, we will consider reflected backward problems with resistance as well. This class of RBSDEs possess...
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作者：Doney, R. A.; Griffin, Philip S.
作者单位：University of Manchester; Syracuse University
摘要：The reflected process of a random walk or Levy process arises in many areas of applied probability, and a question of particular interest is how the tail of the distribution of the heights of the excursions away from zero behaves asymptotically. The Levy analogue of this is the tail behaviour of the characteristic measure of the height of an excursion. Apparently, the only case where this is known is when Cramer's condition hold. Here, we establish the asymptotic behaviour for a large class of...
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作者：Cetin, Umut
作者单位：University of London; London School Economics & Political Science
摘要：We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the first exit times of diffusions, which is recently characterised by Karatzas and Ruf [Probab. Theory Related Fields 164 (2016) 1027-1069] as the minimal solution of an appropriate Cauchy problem under more stringent conditions. A particular limit of these transf...
