Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space
We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fock scale. The noncommutative algebra of relatively (exponentially) bounded nonadapted quantum stochastic processes is st...
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| creator | Belavkin, Viacheslav P Brown, Matthew F |
| description | We study the continuity property of multiple Q-adapted quantum stochastic
integrals with respect to noncommuting integrands given by the non-adapted
multiple integral kernels in Fock scale. The noncommutative algebra of
relatively (exponentially) bounded nonadapted quantum stochastic processes is
studied in the kernel form as introduced by Belavkin in 1991. The differential
Q-adapted formula generalizing Ito product formula for adapted integrals is
presented in both strong and weak sense as a particular case of the quantum
stochastic nonadapted Ito formula. |
| doi_str_mv | 10.48550/arxiv.1112.0159 |
| format | Article |
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integrals with respect to noncommuting integrands given by the non-adapted
multiple integral kernels in Fock scale. The noncommutative algebra of
relatively (exponentially) bounded nonadapted quantum stochastic processes is
studied in the kernel form as introduced by Belavkin in 1991. The differential
Q-adapted formula generalizing Ito product formula for adapted integrals is
presented in both strong and weak sense as a particular case of the quantum
stochastic nonadapted Ito formula.</description><identifier>DOI: 10.48550/arxiv.1112.0159</identifier><language>eng</language><subject>Mathematics - Mathematical Physics ; Mathematics - Quantum Algebra ; Physics - Mathematical Physics ; Physics - Quantum Physics</subject><creationdate>2011-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1112.0159$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1112.0159$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Belavkin, Viacheslav P</creatorcontrib><creatorcontrib>Brown, Matthew F</creatorcontrib><title>Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space</title><description>We study the continuity property of multiple Q-adapted quantum stochastic
integrals with respect to noncommuting integrands given by the non-adapted
multiple integral kernels in Fock scale. The noncommutative algebra of
relatively (exponentially) bounded nonadapted quantum stochastic processes is
studied in the kernel form as introduced by Belavkin in 1991. The differential
Q-adapted formula generalizing Ito product formula for adapted integrals is
presented in both strong and weak sense as a particular case of the quantum
stochastic nonadapted Ito formula.</description><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Quantum Algebra</subject><subject>Physics - Mathematical Physics</subject><subject>Physics - Quantum Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7FOwzAURb0woMLOhPwDCbYTt_FYRRQqFRBq9_DybLcWThw5TgV_TwpMV1e690iHkDvO8rKSkj1A_HLnnHMucsaluiYfL5NPbvCGvmdrDUMymm77ZI4R_Eihn1sKdBNiN3mgwdLX0GPouilBcmdD9yngCcbkkNbgcfLTSF0_H_CT7gdAc0Ou7Iwyt_-5IIfN46F-znZvT9t6vctgKVVWMSFWCEsuhbBcal0yYdFKq02pmSlWoDhabAFZ0TLZgpmHyFVVgpJVaYsFuf_D_ho2Q3QdxO_mYtpcTIsfI9VPCw</recordid><startdate>20111201</startdate><enddate>20111201</enddate><creator>Belavkin, Viacheslav P</creator><creator>Brown, Matthew F</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20111201</creationdate><title>Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space</title><author>Belavkin, Viacheslav P ; Brown, Matthew F</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a659-80227ca61522f15dd402fcf5fde4d0e37a91cfcbac03b05bae522c1984a9584f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Quantum Algebra</topic><topic>Physics - Mathematical Physics</topic><topic>Physics - Quantum Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Belavkin, Viacheslav P</creatorcontrib><creatorcontrib>Brown, Matthew F</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Belavkin, Viacheslav P</au><au>Brown, Matthew F</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space</atitle><date>2011-12-01</date><risdate>2011</risdate><abstract>We study the continuity property of multiple Q-adapted quantum stochastic
integrals with respect to noncommuting integrands given by the non-adapted
multiple integral kernels in Fock scale. The noncommutative algebra of
relatively (exponentially) bounded nonadapted quantum stochastic processes is
studied in the kernel form as introduced by Belavkin in 1991. The differential
Q-adapted formula generalizing Ito product formula for adapted integrals is
presented in both strong and weak sense as a particular case of the quantum
stochastic nonadapted Ito formula.</abstract><doi>10.48550/arxiv.1112.0159</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Mathematical Physics Mathematics - Quantum Algebra Physics - Mathematical Physics Physics - Quantum Physics |
| title | Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space |
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