DC Field | Value | Language |
---|---|---|
dc.contributor.author | Jung, Paul | ko |
dc.contributor.author | Markowsky, Greg | ko |
dc.date.accessioned | 2016-10-04T09:00:13Z | - |
dc.date.available | 2016-10-04T09:00:13Z | - |
dc.date.created | 2016-09-08 | - |
dc.date.created | 2016-09-08 | - |
dc.date.created | 2016-09-08 | - |
dc.date.created | 2016-09-08 | - |
dc.date.issued | 2013-07 | - |
dc.identifier.citation | ANNALS OF PROBABILITY, v.41, no.4, pp.2682 - 2708 | - |
dc.identifier.issn | 0091-1798 | - |
dc.identifier.uri | http://hdl.handle.net/10203/213194 | - |
dc.description.abstract | For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the so-called iterated Brownian motion. Khoshnevisan and Lewis [Ann. Appl. Probab. 9 (1999) 629-667] suggested "the existence of a form of measure-theoretic duality" between iterated Brownian motion and a Brownian motion in random scenery. We show that a random walk at random time can be considered a random walk in "alternating" scenery, thus hinting at a mechanism behind this duality. Following Cohen and Samorodnitsky [Ann. Appl. Probab. 16 (2006) 1432-1461], we also consider alternating random reward schema associated to random walks at random times. Whereas random reward schema scale to local time fractional stable motions, we show that the alternating random reward schema scale to indicator fractional stable motions. Finally, we show that one may recursively "subordinate" random time processes to get new local time and indicator fractional stable motions and new stable processes in random scenery or at random times. When alpha = 2, the fractional stable motions given by the recursion are fractional Brownian motions with dyadic H is an element of (0, 1). Also, we see that "un-subordinating" via a time-change allows one to, in some sense, extract Brownian motion from fractional Brownian motions with H < 1/2 | - |
dc.language | English | - |
dc.publisher | INST MATHEMATICAL STATISTICS | - |
dc.title | RANDOM WALKS AT RANDOM TIMES: CONVERGENCE TO ITERATED LEVY MOTION, FRACTIONAL STABLE MOTIONS, AND OTHER SELF-SIMILAR PROCESSES | - |
dc.type | Article | - |
dc.identifier.wosid | 000322353200008 | - |
dc.identifier.scopusid | 2-s2.0-84881539565 | - |
dc.type.rims | ART | - |
dc.citation.volume | 41 | - |
dc.citation.issue | 4 | - |
dc.citation.beginningpage | 2682 | - |
dc.citation.endingpage | 2708 | - |
dc.citation.publicationname | ANNALS OF PROBABILITY | - |
dc.identifier.doi | 10.1214/12-AOP770 | - |
dc.contributor.localauthor | Jung, Paul | - |
dc.contributor.nonIdAuthor | Markowsky, Greg | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Fractional Brownian motion | - |
dc.subject.keywordAuthor | random walk in random scenery | - |
dc.subject.keywordAuthor | random reward schema | - |
dc.subject.keywordAuthor | local time fractional stable motion | - |
dc.subject.keywordAuthor | self-similar process | - |
dc.subject.keywordAuthor | iterated process | - |
dc.subject.keywordPlus | BROWNIAN-MOTION | - |
dc.subject.keywordPlus | RANDOM SCENERY | - |
dc.subject.keywordPlus | LOCAL-TIMES | - |
dc.subject.keywordPlus | LIMIT-THEOREM | - |
dc.subject.keywordPlus | LOGARITHM | - |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.