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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...
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作者：Baurdoux, Erik J.; Pedraza, Jose M.
作者单位：University of London; London School Economics & Political Science; University of Manchester
摘要：Given a spectrally negative Levy process X drifting to infinity, (inspired on the early ideas of Shiryaev (2002)) we are interested in finding a stopping time that minimises the Lp distance (p > 1) with g, the last time X is negative. The solution is substantially more difficult compared to the case p = 1, for which it was shown by Baurdoux and Pedraza (2020) that it is optimal to stop as soon as X exceeds a constant barrier. In the case of p > 1 treated here, we prove that solving this optima...
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作者：Erignoux, Clement; Simon, Marielle; Zhao, Linjie
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lille; Inria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Huazhong University of Science & Technology
摘要：We derive the hydrodynamic limit for two degenerate lattice gases, the facilitated exclusion process (FEP) and the facilitated zero-range process (FZRP), both in the symmetric and the asymmetric case. For both processes, the hydrodynamic limit in the symmetric case takes the form of a diffusive Stefan problem, whereas the asymmetric case is characterized by a hyperbolic Stefan problem. Although the FZRP is attractive, a property that we extensively use to derive its hydrodynamic limits in both...
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作者：Hening, Alexandru; Qi, Weiwei; Shen, Zhongwei; Yi, Yingfei
作者单位：Texas A&M University System; Texas A&M University Kingsville; University of Alberta
摘要：The present paper is devoted to the study of the long term dynamics of diffusion processes modelling a single species that experiences both demographic and environmental stochasticity. In our setting, the long term dynamics of the diffusion process in the absence of demographic stochasticity is determined by the sign of Lambda(0), the external Lyapunov exponent, as follows: Lambda(0 )< 0 implies (asymptotic) extinction and Lambda(0 )> 0 implies convergence to a unique positive stationary distr...
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作者：Itkin, David; Larsson, Martin
作者单位：Imperial College London; Carnegie Mellon University
摘要：We propose a unified approach to several problems in stochastic portfolio theory (SPT), which is a framework for equity markets with a large number d of stocks. Our approach combines open markets , where trading is confined to the top N capitalized stocks as well as the market portfolio consisting of all d assets, with a parametric family of models which we call hybrid Jacobi processes . We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use these r...
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作者：Bresler, Guy; Nagaraj, Dheeraj; Nichani, Eshaan
作者单位：Massachusetts Institute of Technology (MIT); Alphabet Inc.; Google Incorporated; Princeton University
摘要：In this paper, we consider the problem of sampling from the low temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et al. showed that any local Markov chain suffers from an exponentially large mixing time due to metastable states. We instead consider metastable mixing, a notion of approximate mixing relative to the stationary distribution, for which it turns out to suffice to mix only within a collection of metastable states. We s...
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作者：Brueckerhoff, Martin; Huesmann, Martin
作者单位：University of Munster
摘要：In this article, we show an intimate connection between two objects in probability theory, which received some attention in the last years: shadows of measures and barrier solutions to the Skorokhod embedding problem (SEP). The shadow of a measure mu in the measure. is the key object in the construction of the left-curtain coupling and its siblings in martingale optimal transport by Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106; Trans. Amer. Math. Soc. 374 (2021) 4973-5002). Many promin...
