Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces
We study the weak convergence of the family of processes { V n ( t )} n ∈ℕ defined by where { θ n ( u )} n ∈ℕ is a family of processes converging in law to a Brownian motion, as n →∞. We consider two cases of { θ n }. First, we construct θ n based on the well-known Donsker’s theorem and show that {...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2012-02, Vol.38 (1-2), p.601-615 |
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| container_title | Journal of applied mathematics & computing |
| container_volume | 38 |
| creator | Dai, Hongshuai |
| description | We study the weak convergence of the family of processes {
V
n
(
t
)}
n
∈ℕ
defined by
where {
θ
n
(
u
)}
n
∈ℕ
is a family of processes converging in law to a Brownian motion, as
n
→∞. We consider two cases of {
θ
n
}. First, we construct
θ
n
based on the well-known Donsker’s theorem and show that {
V
n
(
t
)}
n
∈ℕ
converges in law to a multifractional Brownian motion of Riemann-Liouville type, as
n
→∞. Second, we construct
θ
n
based on a Poisson process, and then show that a multifractional Brownian motion of Riemann-Liouville type can be approximated in law by {
V
n
(
t
)}
n
∈ℕ
. |
| doi_str_mv | 10.1007/s12190-011-0499-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1019633139</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1019633139</sourcerecordid><originalsourceid>FETCH-LOGICAL-c348t-6d1da9dc5e19fc19b2344fd36d1ff2ed4c73e9f8a0e8fdac6478760884fe36853</originalsourceid><addsrcrecordid>eNp1kEtLAzEUhQdRsFZ_gLvgyk00j3kkSyu-oCCI4kpCzNyU1JmkJjOV_ntTKgiCq1wO3zmQryhOKbmghDSXiTIqCSaUYlJKiZu9YkJFXWFGRLWf70oKXOXgsDhKaUlI3UgiJ8XbK-gPZIJfQ1yAN4CGgPqxG5yN2gwueN2hWQxf3mmP-rBNULDoyUGvvcdzF8a167rc26wAOY9mkMIapZU2kI6LA6u7BCc_77R4ub15vr7H88e7h-urOTa8FAOuW9pq2ZoKqLSGynfGy9K2POfWMmhL03CQVmgCwrba1GUjmpoIUVrgtaj4tDjf7a5i-BwhDap3yUDXaQ9hTIoSKmvOKZcZPfuDLsMY8y-TkpRJJhhjGaI7yMSQUgSrVtH1Om7yktr6VjvfKvtWW9-qyR2266TM-gXE3-H_S98PUYPR</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>912928222</pqid></control><display><type>article</type><title>Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces</title><source>SpringerNature Journals</source><creator>Dai, Hongshuai</creator><creatorcontrib>Dai, Hongshuai</creatorcontrib><description>We study the weak convergence of the family of processes {
V
n
(
t
)}
n
∈ℕ
defined by
where {
θ
n
(
u
)}
n
∈ℕ
is a family of processes converging in law to a Brownian motion, as
n
→∞. We consider two cases of {
θ
n
}. First, we construct
θ
n
based on the well-known Donsker’s theorem and show that {
V
n
(
t
)}
n
∈ℕ
converges in law to a multifractional Brownian motion of Riemann-Liouville type, as
n
→∞. Second, we construct
θ
n
based on a Poisson process, and then show that a multifractional Brownian motion of Riemann-Liouville type can be approximated in law by {
V
n
(
t
)}
n
∈ℕ
.</description><identifier>ISSN: 1598-5865</identifier><identifier>EISSN: 1865-2085</identifier><identifier>DOI: 10.1007/s12190-011-0499-7</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Applied mathematics ; Approximation ; Banach spaces ; Brownian motion ; Computational Mathematics and Numerical Analysis ; Construction ; Convergence ; INT ; Law ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical functions ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Poisson distribution ; Random variables ; Studies ; Theorems ; Theory of Computation</subject><ispartof>Journal of applied mathematics & computing, 2012-02, Vol.38 (1-2), p.601-615</ispartof><rights>Korean Society for Computational and Applied Mathematics 2011</rights><rights>Korean Society for Computational and Applied Mathematics 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c348t-6d1da9dc5e19fc19b2344fd36d1ff2ed4c73e9f8a0e8fdac6478760884fe36853</citedby><cites>FETCH-LOGICAL-c348t-6d1da9dc5e19fc19b2344fd36d1ff2ed4c73e9f8a0e8fdac6478760884fe36853</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12190-011-0499-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12190-011-0499-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27928,27929,41492,42561,51323</link.rule.ids></links><search><creatorcontrib>Dai, Hongshuai</creatorcontrib><title>Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces</title><title>Journal of applied mathematics & computing</title><addtitle>J. Appl. Math. Comput</addtitle><description>We study the weak convergence of the family of processes {
V
n
(
t
)}
n
∈ℕ
defined by
where {
θ
n
(
u
)}
n
∈ℕ
is a family of processes converging in law to a Brownian motion, as
n
→∞. We consider two cases of {
θ
n
}. First, we construct
θ
n
based on the well-known Donsker’s theorem and show that {
V
n
(
t
)}
n
∈ℕ
converges in law to a multifractional Brownian motion of Riemann-Liouville type, as
n
→∞. Second, we construct
θ
n
based on a Poisson process, and then show that a multifractional Brownian motion of Riemann-Liouville type can be approximated in law by {
V
n
(
t
)}
n
∈ℕ
.</description><subject>Applied mathematics</subject><subject>Approximation</subject><subject>Banach spaces</subject><subject>Brownian motion</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Construction</subject><subject>Convergence</subject><subject>INT</subject><subject>Law</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical functions</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Poisson distribution</subject><subject>Random variables</subject><subject>Studies</subject><subject>Theorems</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kEtLAzEUhQdRsFZ_gLvgyk00j3kkSyu-oCCI4kpCzNyU1JmkJjOV_ntTKgiCq1wO3zmQryhOKbmghDSXiTIqCSaUYlJKiZu9YkJFXWFGRLWf70oKXOXgsDhKaUlI3UgiJ8XbK-gPZIJfQ1yAN4CGgPqxG5yN2gwueN2hWQxf3mmP-rBNULDoyUGvvcdzF8a167rc26wAOY9mkMIapZU2kI6LA6u7BCc_77R4ub15vr7H88e7h-urOTa8FAOuW9pq2ZoKqLSGynfGy9K2POfWMmhL03CQVmgCwrba1GUjmpoIUVrgtaj4tDjf7a5i-BwhDap3yUDXaQ9hTIoSKmvOKZcZPfuDLsMY8y-TkpRJJhhjGaI7yMSQUgSrVtH1Om7yktr6VjvfKvtWW9-qyR2266TM-gXE3-H_S98PUYPR</recordid><startdate>20120201</startdate><enddate>20120201</enddate><creator>Dai, 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convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces</title><author>Dai, Hongshuai</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c348t-6d1da9dc5e19fc19b2344fd36d1ff2ed4c73e9f8a0e8fdac6478760884fe36853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Applied mathematics</topic><topic>Approximation</topic><topic>Banach spaces</topic><topic>Brownian motion</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Construction</topic><topic>Convergence</topic><topic>INT</topic><topic>Law</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical functions</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Poisson distribution</topic><topic>Random variables</topic><topic>Studies</topic><topic>Theorems</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dai, Hongshuai</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) 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Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dai, Hongshuai</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><date>2012-02-01</date><risdate>2012</risdate><volume>38</volume><issue>1-2</issue><spage>601</spage><epage>615</epage><pages>601-615</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>We study the weak convergence of the family of processes {
V
n
(
t
)}
n
∈ℕ
defined by
where {
θ
n
(
u
)}
n
∈ℕ
is a family of processes converging in law to a Brownian motion, as
n
→∞. We consider two cases of {
θ
n
}. First, we construct
θ
n
based on the well-known Donsker’s theorem and show that {
V
n
(
t
)}
n
∈ℕ
converges in law to a multifractional Brownian motion of Riemann-Liouville type, as
n
→∞. Second, we construct
θ
n
based on a Poisson process, and then show that a multifractional Brownian motion of Riemann-Liouville type can be approximated in law by {
V
n
(
t
)}
n
∈ℕ
.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s12190-011-0499-7</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1598-5865 |
| ispartof | Journal of applied mathematics & computing, 2012-02, Vol.38 (1-2), p.601-615 |
| issn | 1598-5865 1865-2085 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1019633139 |
| source | SpringerNature Journals |
| subjects | Applied mathematics Approximation Banach spaces Brownian motion Computational Mathematics and Numerical Analysis Construction Convergence INT Law Mathematical analysis Mathematical and Computational Engineering Mathematical functions Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Poisson distribution Random variables Studies Theorems Theory of Computation |
| title | Weak convergence to multifractional Brownian motion of Riemann-Liouville type in Besov spaces |
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