Sample Path Properties of the Local Time of Multifractional Brownian Motion
We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^{H}=(B^{H(t)}(t),t\in {\Bbb R}^{+})$ . An analogue of Chung's law of the iterated logarithm is studied for $B^{H}$ and used to obtain the pointwise Hölder exponent of t...
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| Veröffentlicht in: | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability 2007-08, Vol.13 (3), p.849-867 |
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| container_end_page | 867 |
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| container_issue | 3 |
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| container_title | Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability |
| container_volume | 13 |
| creator | Boufoussi, Brahim Dozzi, Marco Guerbaz, Raby |
| description | We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^{H}=(B^{H(t)}(t),t\in {\Bbb R}^{+})$ . An analogue of Chung's law of the iterated logarithm is studied for $B^{H}$ and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^{H}$ . |
| doi_str_mv | 10.3150/07-BEJ6140 |
| format | Article |
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An analogue of Chung's law of the iterated logarithm is studied for $B^{H}$ and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^{H}$ .</description><identifier>ISSN: 1350-7265</identifier><identifier>DOI: 10.3150/07-BEJ6140</identifier><language>eng</language><publisher>International Statistics Institute / Bernoulli Society</publisher><subject>Brownian motion ; Chung-type law of iterated logarithm ; Covariance matrices ; Hausdorff dimensions ; local asymptotic self-similarity ; local times ; Logarithms ; Mathematical functions ; Mathematical independent variables ; Mathematics ; multifractional Brownian motion ; Perceptron convergence procedure ; Probability ; Stochastic processes</subject><ispartof>Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, 2007-08, Vol.13 (3), p.849-867</ispartof><rights>Copyright 2007 International Statistical Institute/Bernoulli Society</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><rights>Copyright 2007 Bernoulli Society for Mathematical Statistics and Probability</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c379t-9f5f7439d400c7e56b59199ac1fff0362815e16c4ecd57a43e1ea317d20362ed3</citedby><cites>FETCH-LOGICAL-c379t-9f5f7439d400c7e56b59199ac1fff0362815e16c4ecd57a43e1ea317d20362ed3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/25464908$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/25464908$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,776,780,799,828,881,921,27901,27902,57992,57996,58225,58229</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00098675$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Boufoussi, Brahim</creatorcontrib><creatorcontrib>Dozzi, Marco</creatorcontrib><creatorcontrib>Guerbaz, Raby</creatorcontrib><title>Sample Path Properties of the Local Time of Multifractional Brownian Motion</title><title>Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability</title><description>We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^{H}=(B^{H(t)}(t),t\in {\Bbb R}^{+})$ . An analogue of Chung's law of the iterated logarithm is studied for $B^{H}$ and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^{H}$ .</description><subject>Brownian motion</subject><subject>Chung-type law of iterated logarithm</subject><subject>Covariance matrices</subject><subject>Hausdorff dimensions</subject><subject>local asymptotic self-similarity</subject><subject>local times</subject><subject>Logarithms</subject><subject>Mathematical functions</subject><subject>Mathematical independent variables</subject><subject>Mathematics</subject><subject>multifractional Brownian motion</subject><subject>Perceptron convergence procedure</subject><subject>Probability</subject><subject>Stochastic processes</subject><issn>1350-7265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNpVkE1Lw0AQhnNQsFYv3oVcFaKz2a_kJLVUq6ZYsD0v280u3ZB2y2ar-O9NSCh4GnjmmXfgjaIbBA8YUXgEnjzP3hkicBaNEKaQ8JTRi-iyaSoARBiDUfTxJXeHWsdLGbbx0ruD9sHqJnYmDlsdF07JOl7Zne7I4lgHa7xUwbp9y5-9-9lbuY8XriNX0bmRdaOvhzmO1i-z1XSeFJ-vb9NJkSjM85DkhhpOcF4SAMU1ZRuaozyXChljALM0Q1QjpohWJeWSYI20xIiXabfUJR5HT33uwbtKq6CPqralOHi7k_5XOGnFdF0MdBibSiCUMQqY5NAm3PUJW1n_u5tPCtExAMgzxuk3bt373lXeNY3X5nSAQHRFC-BiKLqVb3u5aoLzJzOlhLV_M_wH9hd7IQ</recordid><startdate>20070801</startdate><enddate>20070801</enddate><creator>Boufoussi, Brahim</creator><creator>Dozzi, Marco</creator><creator>Guerbaz, Raby</creator><general>International Statistics Institute / Bernoulli Society</general><general>Bernoulli Society for Mathematical Statistics and Probability</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20070801</creationdate><title>Sample Path Properties of the Local Time of Multifractional Brownian Motion</title><author>Boufoussi, Brahim ; Dozzi, Marco ; Guerbaz, Raby</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c379t-9f5f7439d400c7e56b59199ac1fff0362815e16c4ecd57a43e1ea317d20362ed3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Brownian motion</topic><topic>Chung-type law of iterated logarithm</topic><topic>Covariance matrices</topic><topic>Hausdorff dimensions</topic><topic>local asymptotic self-similarity</topic><topic>local times</topic><topic>Logarithms</topic><topic>Mathematical functions</topic><topic>Mathematical independent variables</topic><topic>Mathematics</topic><topic>multifractional Brownian motion</topic><topic>Perceptron convergence procedure</topic><topic>Probability</topic><topic>Stochastic processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Boufoussi, Brahim</creatorcontrib><creatorcontrib>Dozzi, Marco</creatorcontrib><creatorcontrib>Guerbaz, Raby</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Boufoussi, Brahim</au><au>Dozzi, Marco</au><au>Guerbaz, Raby</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Sample Path Properties of the Local Time of Multifractional Brownian Motion</atitle><jtitle>Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability</jtitle><date>2007-08-01</date><risdate>2007</risdate><volume>13</volume><issue>3</issue><spage>849</spage><epage>867</epage><pages>849-867</pages><issn>1350-7265</issn><abstract>We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, $B^{H}=(B^{H(t)}(t),t\in {\Bbb R}^{+})$ . An analogue of Chung's law of the iterated logarithm is studied for $B^{H}$ and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be satisfied by the local time of $B^{H}$ .</abstract><pub>International Statistics Institute / Bernoulli Society</pub><doi>10.3150/07-BEJ6140</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
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| source | Jstor Complete Legacy; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | Brownian motion Chung-type law of iterated logarithm Covariance matrices Hausdorff dimensions local asymptotic self-similarity local times Logarithms Mathematical functions Mathematical independent variables Mathematics multifractional Brownian motion Perceptron convergence procedure Probability Stochastic processes |
| title | Sample Path Properties of the Local Time of Multifractional Brownian Motion |
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