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作者：Gassiat, Paul; Seeger, Benjamin
作者单位：Universite PSL; Universite Paris-Dauphine; University of Texas System; University of Texas Austin
摘要：We generalize the notion of pathwise viscosity solutions, put forward by Lions and Souganidis to study fully nonlinear stochastic partial differential equations, to equations set on a sub-domain with Neumann boundary conditions. Under a convexity assumption on the domain, we obtain a comparison theorem which yields existence and uniqueness of solutions as well as continuity with respect to the driving noise. As an application, we study the long time behaviour of a stochastically perturbed mean...
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作者：Bayraktar, Erhan; Yao, Song
作者单位：University of Michigan System; University of Michigan; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an arbitrary probability setting is equivalent to the constrained problem in weak formulation (an optimization over joint laws of stopping rules with Brownian motion and state dynamics on an enlarged canonical space), and thus the OSEC value is independent of a spe...
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作者：Bou-Rabee, Ahmed
作者单位：University of Chicago
摘要：We study scaling limits of exploding Abelian sandpiles using ideas from percolation and front propagation in random media. We establish sufficient conditions under which a limit shape exists and show via a family of counter-examples that convergence may not occur in general. A corollary of our proof is a simple criterion for determining if a sandpile is explosive; this strengthens a result of Fey, Levine and Peres (J. Stat. Phys. (2010) 138 143-159).
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作者：Ertel, Sebastian W.; Stannat, Wilhelm
作者单位：Technical University of Berlin
摘要：Ensemble Kalman-Bucy filters (EnKBFs) are an important tool in data assimilation that aim to approximate the posterior distribution for continuous time filtering problems using an ensemble of interacting particles. In this work we extend a previously derived unifying framework for consistent representations of the posterior distribution to correlated observation noise and use these representations to derive an EnKBF suitable for this setting as a constant gain approximation of these optimal fi...
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作者：Dubach, Guillaume
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We present general links between statistics of non-Hermitian random matrices and the distribution of the number of cycles of some specific random permutations. In particular, we derive explicit formulas for the generating functions of the number of cycles in the commutator [ sigma, tau] ] = sigma tau sigma (- 1 )tau (- 1) where sigma is uniformly distributed, and tau is either one cycle, the product of many transpositions, or the product of two cycles of same size, the latter case being a new ...
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作者：Hong, Wei; Hu, Shanshan; Liu, Wei
作者单位：Jiangsu Normal University; University of Bielefeld
摘要：In this paper we mainly investigate the strong and weak well-posedness of a class of McKean-Vlasov stochastic (partial) differential equations. The main existence and uniqueness results state that we only need to impose some local assumptions on the coefficients, that is, locally monotone condition both in state variable and distribution variable, which cause some essential difficulty since the coefficients of McKean-Vlasov stochastic equations typically are nonlocal. Furthermore, the large de...
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作者：Kim, Inwon C.; Kim, Young-Heon
作者单位：University of California System; University of California Los Angeles; University of British Columbia
摘要：e formulate and solve a free target optimal Brownian stopping prob-lem from a given distribution while the target distribution is free and is con-ditioned to satisfy a given density height constraint. The free target optimiza-tion problem exhibits monotonicity, from which a remarkable universalityfollows, in the sense that the optimal target is independent of its Lagrangiancost type. In particular, the solutions to this optimization problem generatesolutions to both unstable and stable type of...
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作者：Birkner, Matthias; Callegaro, Alice; Cerny, Jiri; Gantert, Nina; Oswald, Pascal
作者单位：Johannes Gutenberg University of Mainz; Technical University of Munich; University of Basel
摘要：We study a discrete-time branching annihilating random walk (BARW) on the d-dimensional lattice. Each particle produces a Poissonian number of offspring with mean mu which independently move to a uniformly chosen site within a fixed distance R from their parent's position. Whenever a site is occupied by at least two particles, all the particles at that site are annihilated. We prove that for any mu > 1 the process survives when R is sufficiently large. For fixed R we show that the process dies...
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作者：Margarint, Vlad; Shekhar, Atul; Yuan, Yizheng
作者单位：University of North Carolina; University of North Carolina Charlotte; Tata Institute of Fundamental Research (TIFR); University of Cambridge
摘要：We prove existence (and simpleness) of the trace for both forward and backward Loewner chains under fairly general conditions on semimartingale drivers. As an application, we show that stochastic Komatu-Loewner evolutions SKLE alpha,b are generated by curves. As another application, motivated by a question of A. Sep & uacute;lveda, we show that for alpha > 3/2 and Brownian motion B, the driving function |B-t |(alpha) generates a simple curve for small t. On a related note we also introduce a c...
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作者：Arman, Andrii; Gao, Pu; Wormald, Nicholas
作者单位：University of Manitoba; University of Waterloo; Monash University
摘要：We give an algorithm which generates a uniformly random contingency table with specified marginals, that is, a matrix with nonnegative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics. When Delta(4) < M/5, where Delta is the maximum of the row and column sums and M is the sum of all entries of the matrix, our algorithm runs in time linear in M in expectation. Most previously published algorithms for this problem are approximate sample...
