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Concrete Representation of Martingales


 
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1. Title Title of document Concrete Representation of Martingales
 
2. Creator Author's name, affiliation, country Stephen Montgomery-Smith; University of Missouri
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) martingale, concrete representation, tangent sequence, condition (C.I.), UMD, Skorohod representation
 
3. Subject Subject classification 60G42, 60H05
 
4. Description Abstract Let $(f_n)$ be a mean zero vector valued martingale sequence. Then there exist vector valued functions $(d_n)$ from $[0,1]^n$ such that $\int_0^1 d_n(x_1,\dots,x_n)\,dx_n = 0$ for almost all $x_1,\dots,x_{n-1}$, and such that the law of $(f_n)$ is the same as the law of $(\sum_{k=1}^n d_k(x_1,\dots,x_k))$. Similar results for tangent sequences and sequences satisfying condition (C.I.) are presented. We also present a weaker version of a result of McConnell that provides a Skorohod like representation for vector valued martingales.
 
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7. Date (YYYY-MM-DD) 1998-12-02
 
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/37
 
10. Identifier Digital Object Identifier 10.1214/EJP.v3-37
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 3
 
12. Language English=en en
 
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