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A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals


 
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1. Title Title of document A Generalized Ito's Formula in Two-Dimensions and Stochastic Lebesgue-Stieltjes Integrals
 
2. Creator Author's name, affiliation, country Chunrong Feng; Loughborough University
 
2. Creator Author's name, affiliation, country Huaizhong Zhao; Loughborough University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) local time; continuous semimartingale; generalized It$hat {rm o}$'s formula; stochastic Lebesgue-Stieltjes integral
 
3. Subject Subject classification 60H05, 60J55
 
4. Description Abstract In this paper, a generalized It${\hat {\rm o}}$'s formula for continuous functions of two-dimensional continuous semimartingales is proved. The formula uses the local time of each coordinate process of the semimartingale, the left space first derivatives and the second derivative $\nabla _1^- \nabla _2^-f$, and the stochastic Lebesgue-Stieltjes integrals of two parameters. The second derivative $\nabla _1^- \nabla _2^-f$ is only assumed to be of locally bounded variation in certain variables. Integration by parts formulae are asserted for the integrals of local times. The two-parameter integral is defined as a natural generalization of both the Ito integral and the Lebesgue-Stieltjes integral through a type of It${\hat {\rm o }}$ isometry formula.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) EPSRC and Loughborough University
 
7. Date (YYYY-MM-DD) 2007-12-23
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/468
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-468
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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