{"title":"平面随机游动和布朗运动凸壳的大偏差","authors":"A. Akopyan, V. Vysotsky","doi":"10.5802/ahl.100","DOIUrl":null,"url":null,"abstract":". — We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give explicit upper and lower bounds for the rate function of the perimeter in terms of the rate function of the increments. These bounds coincide and thus give the rate function for pas optimaux en général.","PeriodicalId":192307,"journal":{"name":"Annales Henri Lebesgue","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Large deviations of convex hulls of planar random walks and Brownian motions\",\"authors\":\"A. Akopyan, V. Vysotsky\",\"doi\":\"10.5802/ahl.100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". — We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give explicit upper and lower bounds for the rate function of the perimeter in terms of the rate function of the increments. These bounds coincide and thus give the rate function for pas optimaux en général.\",\"PeriodicalId\":192307,\"journal\":{\"name\":\"Annales Henri Lebesgue\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Lebesgue\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/ahl.100\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Lebesgue","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/ahl.100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Large deviations of convex hulls of planar random walks and Brownian motions
. — We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give explicit upper and lower bounds for the rate function of the perimeter in terms of the rate function of the increments. These bounds coincide and thus give the rate function for pas optimaux en général.
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