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Electronic Communications in Probability最新文献

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The existence of the least favorable noise 最不利噪声的存在
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp533
Dongzhou Huang
{"title":"The existence of the least favorable noise","authors":"Dongzhou Huang","doi":"10.1214/23-ecp533","DOIUrl":"https://doi.org/10.1214/23-ecp533","url":null,"abstract":"Suppose that a random variable $X$ of interest is observed. This paper concerns\"the least favorable noise\"$hat{Y}_{epsilon}$, which maximizes the prediction error $E [X - E[X|X+Y]]^2 $ (or minimizes the variance of $E[X| X+Y]$) in the class of $Y$ with $Y$ independent of $X$ and $mathrm{var} Y leq epsilon^2$. This problem was first studied by Ernst, Kagan, and Rogers ([3]). In the present manuscript, we show that the least favorable noise $hat{Y}_{epsilon}$ must exist and that its variance must be $epsilon^2$. The proof of existence relies on a convergence result we develop for variances of conditional expectations. Further, we show that the function $inf_{mathrm{var} Y leq epsilon^2} , mathrm{var} , E[X|X+Y]$ is both strictly decreasing and right continuous in $epsilon$.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47464978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Corrigendum to: The contact process on periodic trees 勘误表：周期树上的接触过程
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp518
Xiangying Huang, R. Durrett
{"title":"Corrigendum to: The contact process on periodic trees","authors":"Xiangying Huang, R. Durrett","doi":"10.1214/23-ecp518","DOIUrl":"https://doi.org/10.1214/23-ecp518","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44393029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments 一类无界环境中定向聚合物弱无序相的矩表征
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp545
Ryoki Fukushima, Stefan Junk
{"title":"Moment characterization of the weak disorder phase for directed polymers in a class of unbounded environments","authors":"Ryoki Fukushima, Stefan Junk","doi":"10.1214/23-ecp545","DOIUrl":"https://doi.org/10.1214/23-ecp545","url":null,"abstract":"For a directed polymer model in random environment, a characterization of the weak disorder phase in terms of the moment of the renormalized partition function has been proved in [S. Junk: Communications in Mathematical Physics 389, 1087–1097 (2022)]. We extend this characterization to a large class of unbounded environments which includes many commonly used distributions.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135958441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The scaling limit of the weakly self-avoiding walk on a high-dimensional torus 高维环面上弱自避行走的尺度极限
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp531
Emmanuel Michta
{"title":"The scaling limit of the weakly self-avoiding walk on a high-dimensional torus","authors":"Emmanuel Michta","doi":"10.1214/23-ecp531","DOIUrl":"https://doi.org/10.1214/23-ecp531","url":null,"abstract":"We prove that the scaling limit of the weakly self-avoiding walk on a d-dimensional discrete torus is Brownian motion on the continuum torus if the length of the rescaled walk is o(V1∕2) where V is the volume (number of points) of the torus and if d>4. We also prove that the diffusion constant of the resulting torus Brownian motion is the same as the diffusion constant of the scaling limit of the usual weakly self-avoiding walk on Zd. This provides further manifestation of the fact that the weakly self-avoiding walk model on the torus does not feel that it is on the torus up until it reaches about V1∕2 steps, which we believe is sharp.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135733740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Brownian snails with removal die out in one dimension 带移除的布朗蜗牛在一维中死亡
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp551
Ivailo Hartarsky, Lyuben Lichev
{"title":"Brownian snails with removal die out in one dimension","authors":"Ivailo Hartarsky, Lyuben Lichev","doi":"10.1214/23-ecp551","DOIUrl":"https://doi.org/10.1214/23-ecp551","url":null,"abstract":"Brownian snails with removal is a spatial epidemic model defined as follows. Initially, a homogeneous Poisson process of susceptible particles on Rd with intensity λ>0 is deposited and a single infected one is added at the origin. Each particle performs an independent standard Brownian motion. Each susceptible particle is infected immediately when it is within distance 1 from an infected particle. Each infected particle is removed at rate α>0, and removed particles remain such forever. Answering a question of Grimmett and Li, we prove that in one dimension, for all values of λ and α, the infection almost surely dies out.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135450721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On smooth approximations in the Wasserstein space 关于Wasserstein空间中的光滑逼近
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ECP538
Andrea Cosso, Mattia Martini
{"title":"On smooth approximations in the Wasserstein space","authors":"Andrea Cosso, Mattia Martini","doi":"10.1214/23-ECP538","DOIUrl":"https://doi.org/10.1214/23-ECP538","url":null,"abstract":"In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are able to construct a sequence of infinitely differentiable functions having the same Lipschitz constant as the original function. This solves an open problem raised in [11]. For (resp. twice) continuously differentiable function, we show that our approximation also holds for the first-order derivative (resp. second-order derivatives), therefore solving another open problem raised in [11].","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45296634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Generating discrete uniform distribution from a biased coin using number-theoretic method 用数论方法生成有偏硬币的离散均匀分布
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp537
Xiaoyu Lei
{"title":"Generating discrete uniform distribution from a biased coin using number-theoretic method","authors":"Xiaoyu Lei","doi":"10.1214/23-ecp537","DOIUrl":"https://doi.org/10.1214/23-ecp537","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41951614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the specific relative entropy between martingale diffusions on the line 关于线上鞅扩散之间的特定相对熵
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp548
Julio Backhoff-Veraguas, Clara Unterberger
{"title":"On the specific relative entropy between martingale diffusions on the line","authors":"Julio Backhoff-Veraguas, Clara Unterberger","doi":"10.1214/23-ecp548","DOIUrl":"https://doi.org/10.1214/23-ecp548","url":null,"abstract":"The specific relative entropy, introduced in the Wiener space setting by N. Gantert, allows to quantify the discrepancy between the laws of potentially mutually singular measures. It appears naturally as the large deviations rate function in a randomized version of Donsker’s invariance principle, as well as in a novel transport-information inequality recently derived by H. Föllmer. A conjecture, put forward by the aforementioned authors, concerns a closed form expression for the specific relative entropy between continuous martingale laws in terms of their quadratic variations. We provide a first partial result in this direction, by establishing this conjecture in the case of well-behaved martingale diffusions on the line.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135955011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Competition on Zd driven by branching random walk 由分支随机漫步驱动的Zd竞争
IF 0.5 4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp521
Maria Deijfen, Timo Vilkas
{"title":"Competition on Zd driven by branching random walk","authors":"Maria Deijfen, Timo Vilkas","doi":"10.1214/23-ecp521","DOIUrl":"https://doi.org/10.1214/23-ecp521","url":null,"abstract":"","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49209909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the existence of weak solutions to stochastic Volterra equations 关于随机Volterra方程弱解的存在性
4区 数学
Electronic Communications in Probability Pub Date : 2023-01-01 DOI: 10.1214/23-ecp554
David J. Prömel, David Scheffels
{"title":"On the existence of weak solutions to stochastic Volterra equations","authors":"David J. Prömel, David Scheffels","doi":"10.1214/23-ecp554","DOIUrl":"https://doi.org/10.1214/23-ecp554","url":null,"abstract":"The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented approach is based on a newly formulated local martingale problem associated to stochastic Volterra equations.","PeriodicalId":50543,"journal":{"name":"Electronic Communications in Probability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135704896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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