2023

最新文章

• NONPARAMETRIC LEARNING FOR IMPULSE CONTROL PROBLEMS-EXPLORATION VS. EXPLOITATION AI翻译
  作者：Christensen, Soren; Strauch, Claudia
  作者单位：University of Kiel; Aarhus University
  摘要：One of the fundamental assumptions in stochastic control of continuous time processes is that the dynamics of the underlying (diffusion) process is known. This is, however, usually obviously not fulfilled in practice. On the other hand, over the last decades, a rich theory for nonparametric estimation of the drift (and volatility) for continuous time processes has been developed. The aim of this paper is bringing together techniques from stochastic control with methods from statistics for stoc...
• THE SIZE OF t-CORES AND HOOK LENGTHS OF RANDOM CELLS IN RANDOM PARTITIONS AI翻译
  作者：Ayyer, Arvind; Sinha, Shubham
  作者单位：Indian Institute of Science (IISC) - Bangalore; University of California System; University of California San Diego
  摘要：Fix t >= 2. We first give an asymptotic formula for certain sums of the number of t-cores. We then use this result to compute the distribution of the size of the t-core of a uniformly random partition of an integer n. We show that this converges weakly to a gamma distribution after dividing by root n. As a consequence, we find that the size of the t-core is of the order of root n in expectation. We then apply this result to show that the probability that t divides the hook length of a uniforml...
• SPIKING AND COLLAPSING IN LARGE NOISE LIMITS OF SDES AI翻译
  作者：Bernardin, Cedric; Chetrite, Raphael; Chhaibi, Reda; Najnudel, Joseph; Pellegrini, Clemnt
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：We analyze the strong noise limit of one-dimensional stochastic differ-ential equations (SDEs).Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an intriguing behavior. As the noise grows larger, the solutions exhibit locally a collapsing, that is to say, converge to pure jump processes very reminiscent of a metastability phenomenon. But surprisingly the limiting jump process is decorated by a spike process...
• THE TAP FREE ENERGY FOR HIGH-DIMENSIONAL LINEAR REGRESSION AI翻译
  作者：Qiu, Jiaze; Sen, Subhabrata
  作者单位：Harvard University
  摘要：We derive a variational representation for the log-normalizing constant of the posterior distribution in Bayesian linear regression with a uniform spherical prior and an i.i.d. Gaussian design. We work under the propor-tional asymptotic regime, where the number of observations and the number of features grow at a proportional rate. Our representation holds when the variance of the additive noise is sufficiently large, which corresponds to a high-temperature condition in statistical physics. Th...
• MODEL-FREE MEAN-FIELD REINFORCEMENT LEARNING: MEAN-FIELD MDP AND MEAN-FIELD Q-LEARNING AI翻译
  作者：Carmona, Rene; Lauriere, Mathieu; Tan, Zongjun
  作者单位：Princeton University; New York University; NYU Shanghai; New York University; NYU Shanghai
  摘要：We study infinite horizon discounted mean field control (MFC) prob-lems with common noise through the lens of mean field Markov decision processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual level but also at the level of the population. This common randomization is introduced for the purpose of exploration from a reinforcement learning (RL) paradigm. It also allows us to establish connec-tions between both closed-loop and open-loop policies for M...
• THE COALESCENT STRUCTURE OF UNIFORM AND POISSON SAMPLES FROM MULTITYPE BRANCHING PROCESSES AI翻译
  作者：Johnston, Samuel g. g.; Lambert, Amaury
  作者单位：University of London; King's College London; Universite Paris Cite; Sorbonne Universite
  摘要：We introduce a Poissonization method to study the coalescent structure of uniform samples from branching processes. This method relies on the simple observation that a uniform sample of size k taken from a random set with positive Lebesgue measure may be represented as a mixture of Poisson samples with rate lambda and mixing measure k d lambda/lambda. We develop a multitype analogue of this mixture representation, and use it to characterise the coalescent structure of multitype continuous-stat...
• CONTINUITY OF THE MARTINGALE OPTIMAL TRANSPORT PROBLEM ON THE REAL LINE AI翻译
  作者：Wiesel, Johannes
  作者单位：Carnegie Mellon University
  摘要：We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the set of martingale couplings with the same marginals. As a corollary we obtain an independent proof of sufficiency of the monotonicity principle established in Beiglbock and Juillet (Ann. Probab. 44 (2016) 42- 106) for cost functions of polynomial growth.
• FLUCTUATION BOUNDS FOR CONTINUOUS TIME BRANCHING PROCESSES AND EVOLUTION OF GROWING TREES WITH A CHANGE POINT AI翻译
  作者：Banerjee, Sayan; Bhamidi, Shankar; Carmichael, Iain
  作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of California System; University of California Berkeley
  摘要：We consider dynamic random trees constructed using an attachment function f : N & RARR; R+ where, at each step of the evolution, a new vertex attaches to an existing vertex v in the current tree with probability propor-tional to f (degree(v)). We explore the effect of a change point in the sys-tem; the dynamics are initially driven by a function f until the tree reaches size & tau;(n) & ISIN; (0, n), at which point the attachment function switches to another function, g, until the tree reaches...
• DENSE MULTIGRAPHON-VALUED STOCHASTIC PROCESSES AND EDGE-CHANGING DYNAMICS IN THE CONFIGURATION MODEL AI翻译
  作者：Rollin, Adrian; Zhang, Zhuo-Song
  作者单位：National University of Singapore; Southern University of Science & Technology
  摘要：Time-evolving random graph models have appeared and have been studied in various fields of research over the past decades. However, the rigorous mathematical treatment of large graphs and their limits at the process-level is still in its infancy. In this article, we adapt the approach of Athreya, den ting of multigraphs and multigraphons, introduced by Kolossvary and Rath (Acta Math. Hungar. 130 (2011) 1-34). We then generalise the work of Rath namics on the configuration model-in contrast to ...
• INVARIANCE PRINCIPLES FOR INTEGRATED RANDOM WALKS CONDITIONED TO STAY POSITIVE AI翻译
  作者：Baer, Michael; Duraj, Jetlir; Wachtel, Vitali
  作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; University of Bielefeld
  摘要：Let S (n) be a centered random walk with finite second moment. We con-sider the integrated random walk T (n) = S(0) + S(1) + center dot center dot center dot + S(n). We prove invariance principles for the meander and for the bridge of this process, un-der the condition that the integrated random walk remains positive. Further-more, we prove the functional convergence of its Doob's h-transform to the h-transform of the Kolmogorov diffusion conditioned to stay positive.