Anticipative Stochastic Differential Equations with Non-smooth Diffusion Coefficient
(ProQuest: Abstract omitted; see image)[PUBLICATION ABSTRACT]
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| Published in | Acta mathematica Sinica. English series Vol. 22; no. 5; pp. 1473 - 1480 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Springer Nature B.V
01.09.2006
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| Subjects | |
| Online Access | Get full text |
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| Abstract | (ProQuest: Abstract omitted; see image)[PUBLICATION ABSTRACT] |
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| AbstractList | In this paper we prove the existence and uniqueness of the solutions to the one-dimensional linear stochastic differential equation with Skorohod integral X t ( w ) = eta ( w ) + [int] 0 t a s X s ( w ) d \bf W s + [int] 0 t b s X s ( w ) ds , t [isin] [ 0,1 ] , where (W sub( )s is the canonical Wiener process defined on the standard Wiener space ( fancyscript W , , mu ), a is non-smooth and adapted, but eta and b may be anticipating to the filtration generated by (W sub( )s. The intention of the paper is to eliminate the regularity of the diffusion coefficient a in the Malliavin sense, in the existing literature. The idea is to approach the non-smooth diffusion coefficient a by smooth ones. (ProQuest: Abstract omitted; see image)[PUBLICATION ABSTRACT] |
| Author | Liang, Zong Xia |
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| CitedBy_id | crossref_primary_10_18654_1000_0569_2020_11_01 crossref_primary_10_18654_1000_0569_2020_07_01 crossref_primary_10_18654_1000_0569_2020_07_08 |
| Cites_doi | 10.1007/BF00353876 10.1007/BF01206230 10.1007/BF01192163 10.1080/17442508408833303 10.1016/0022-1236(74)90017-2 10.1007/BF00341281 10.1007/BF01193054 10.1214/aop/1176989392 |
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| DOI | 10.1007/s10114-005-0816-x |
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| References | Buckdahn (816_CR6) 1992; 93 Buckdahn (816_CR5) 1991; 90 Ocone (816_CR2) 1989; 82 Barlow (816_CR10) 1984; 12 Ocone (816_CR3) 1989; 25 Enchev (816_CR8) 1993; 21 Buckdahn (816_CR7) 1994; 99 Shioto (816_CR4) 1986; 9 Nualart (816_CR1) 1988; 78 Ramer (816_CR9) 1974; 15 |
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| Snippet | (ProQuest: Abstract omitted; see image)[PUBLICATION ABSTRACT] In this paper we prove the existence and uniqueness of the solutions to the one-dimensional linear stochastic differential equation with Skorohod integral X t... |
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| SubjectTerms | Calculus Differential equations Diffusion coefficient Hypotheses INT Mathematical analysis Random variables Regularity Stochasticity Uniqueness |
| Title | Anticipative Stochastic Differential Equations with Non-smooth Diffusion Coefficient |
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