Doob, Ignatov and Optional Skipping
A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Méch. 71 (1977) 79-94...
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| Veröffentlicht in: | The Annals of probability 2002-10, Vol.30 (4), p.1933-1958 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
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| container_end_page | 1958 |
|---|---|
| container_issue | 4 |
| container_start_page | 1933 |
| container_title | The Annals of probability |
| container_volume | 30 |
| creator | Simons, Gordon Yao, Yi-Ching Yang, Lijian |
| description | A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Méch. 71 (1977) 79-94], unifying and extending aspects of both. |
| doi_str_mv | 10.1214/aop/1039548377 |
| format | Article |
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This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Méch. 71 (1977) 79-94], unifying and extending aspects of both.</description><subject>28D05</subject><subject>60G40</subject><subject>Backward induction</subject><subject>Definiteness</subject><subject>disentangled stopping times</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>Ignatov's theorem</subject><subject>indexical stopping times</subject><subject>Indexicality</subject><subject>Induction assumption</subject><subject>k-records</subject><subject>Logical givens</subject><subject>Mathematical analysis</subject><subject>Mathematical theorems</subject><subject>Mathematics</subject><subject>Measure and integration</subject><subject>optional skipping</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Random variables</subject><subject>records</subject><subject>Sciences and techniques of general use</subject><subject>Stochastic processes</subject><subject>Stopping distances</subject><subject>Truncation</subject><issn>0091-1798</issn><issn>2168-894X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><recordid>eNplUE1LwzAYDqLgnF49eSiIN7sly_dNmV-DwQ468FbepsnIrE1JquC_t2PFHTw98D5fPC9ClwRPyIywKYR2SjDVnCkq5REazYhQudLs_RiNMNYkJ1KrU3SW0hZjLKRkI3T9EEJ5my02DXThO4OmylZt50MDdfb64dvWN5tzdOKgTvZiwDFaPz2-zV_y5ep5Mb9f5oYy3OXAHOFKV32VNNQJpjitFMO0dKXUFhzmDjS3UjAQpKSOaSKxtDtKKMLoGN3tc9sYttZ09svUvira6D8h_hQBfDFfL4frAP3o4jC6j5jsI0wMKUXr_twEF7sv_TfcDJ2QDNQuQmN8OrgY45QL0euu9rpt6kI88Jyr3cRfXA1wBg</recordid><startdate>20021001</startdate><enddate>20021001</enddate><creator>Simons, Gordon</creator><creator>Yao, Yi-Ching</creator><creator>Yang, Lijian</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20021001</creationdate><title>Doob, Ignatov and Optional Skipping</title><author>Simons, Gordon ; Yao, Yi-Ching ; Yang, Lijian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c340t-a4f1589d0097c3f64853d8403bfb79eaf05fa95e764a61b3f491707e9eaf68143</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>28D05</topic><topic>60G40</topic><topic>Backward induction</topic><topic>Definiteness</topic><topic>disentangled stopping times</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>Ignatov's theorem</topic><topic>indexical stopping times</topic><topic>Indexicality</topic><topic>Induction assumption</topic><topic>k-records</topic><topic>Logical givens</topic><topic>Mathematical analysis</topic><topic>Mathematical theorems</topic><topic>Mathematics</topic><topic>Measure and integration</topic><topic>optional skipping</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Random variables</topic><topic>records</topic><topic>Sciences and techniques of general use</topic><topic>Stochastic processes</topic><topic>Stopping distances</topic><topic>Truncation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Simons, Gordon</creatorcontrib><creatorcontrib>Yao, Yi-Ching</creatorcontrib><creatorcontrib>Yang, Lijian</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The Annals of probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Simons, Gordon</au><au>Yao, Yi-Ching</au><au>Yang, Lijian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Doob, Ignatov and Optional Skipping</atitle><jtitle>The Annals of probability</jtitle><date>2002-10-01</date><risdate>2002</risdate><volume>30</volume><issue>4</issue><spage>1933</spage><epage>1958</epage><pages>1933-1958</pages><issn>0091-1798</issn><eissn>2168-894X</eissn><coden>APBYAE</coden><abstract>A general set of distribution-free conditions is described under which an i.i.d. sequence of random variables is preserved under optional skipping. This work is motivated by theorems of J. L. Doob [Ann. of Math. 37 (1936) 363-367] and Z. Ignatov [Annuaire Univ. Sofia Fac. Math. Méch. 71 (1977) 79-94], unifying and extending aspects of both.</abstract><cop>Hayward, CA</cop><pub>Institute of Mathematical Statistics</pub><doi>10.1214/aop/1039548377</doi><tpages>26</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0091-1798 |
| ispartof | The Annals of probability, 2002-10, Vol.30 (4), p.1933-1958 |
| issn | 0091-1798 2168-894X |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_aop_1039548377 |
| source | Jstor Complete Legacy; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | 28D05 60G40 Backward induction Definiteness disentangled stopping times Distribution theory Exact sciences and technology Ignatov's theorem indexical stopping times Indexicality Induction assumption k-records Logical givens Mathematical analysis Mathematical theorems Mathematics Measure and integration optional skipping Probability and statistics Probability theory and stochastic processes Random variables records Sciences and techniques of general use Stochastic processes Stopping distances Truncation |
| title | Doob, Ignatov and Optional Skipping |
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