{"title":"随机测量路径的规律性","authors":"Vadym Radchenko","doi":"arxiv-2409.06497","DOIUrl":null,"url":null,"abstract":"Random functions $\\mu(x)$, generated by values of stochastic measures are\nconsidered. The Besov regularity of the continuous paths of $\\mu(x)$,\n$x\\in[0,1]^d$ is proved. Fourier series expansion of $\\mu(x)$, $x\\in[0,2\\pi]$\nis obtained. These results are proved under weaker conditions than similar\nresults in previous papers.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularity of paths of stochastic measures\",\"authors\":\"Vadym Radchenko\",\"doi\":\"arxiv-2409.06497\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Random functions $\\\\mu(x)$, generated by values of stochastic measures are\\nconsidered. The Besov regularity of the continuous paths of $\\\\mu(x)$,\\n$x\\\\in[0,1]^d$ is proved. Fourier series expansion of $\\\\mu(x)$, $x\\\\in[0,2\\\\pi]$\\nis obtained. These results are proved under weaker conditions than similar\\nresults in previous papers.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"39 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06497\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06497","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Random functions $\mu(x)$, generated by values of stochastic measures are
considered. The Besov regularity of the continuous paths of $\mu(x)$,
$x\in[0,1]^d$ is proved. Fourier series expansion of $\mu(x)$, $x\in[0,2\pi]$
is obtained. These results are proved under weaker conditions than similar
results in previous papers.
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