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On the one-sided Tanaka equation with drift


 
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1. Title Title of document On the one-sided Tanaka equation with drift
 
2. Creator Author's name, affiliation, country Ioannis Karatzas; Intech Investment Management, Columbia University
 
2. Creator Author's name, affiliation, country Albert N. Shiryaev; Steklov Mathematical Institute
 
2. Creator Author's name, affiliation, country Mykhaylo Shkolnikov; Intech Investment Management, Stanford University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Stochastic differential equation, weak existence, weak uniqueness, strong existence, strong uniqueness, Tanaka equation, skew Brownian motion, sticky Brownian motion, comparison theorems for diffusions
 
3. Subject Subject classification 60H10, 60J60, 60J65
 
4. Description Abstract We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift lambda. We observe a dichotomy in terms of the values of the drift parameter: for $\lambda\leq 0$, there exists a strong solution which is pathwise unique, thus also unique in distribution; whereas for $\lambda > 0$, the equation has a unique in distribution weak solution, but no strong solution (and not even a weak solution that spends zero time at the origin). We also show that strength and pathwise uniqueness are restored to the equation via suitable ``Brownian perturbations".
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF Grants DMS-08-06211 and DMS-09-05754.
 
7. Date (YYYY-MM-DD) 2011-10-31
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1665
 
10. Identifier Digital Object Identifier 10.1214/ECP.v16-1665
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 16
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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