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An optimal Skorokhod embedding for diffusions
- Source :
- Stochastic Processes and their Applications. (1):17-39
- Publisher :
- Elsevier B.V.
-
Abstract
- Given a Brownian motion $B_t$ and a general target law $\mu$ (not necessarily centered or even integrable) we show how to construct an embedding of $\mu$ in $B$. This embedding is an extension of an embedding due to Perkins, and is optimal in the sense that it simultaneously minimises the distribution of the maximum and maximises the distribution of the minimum among all embeddings of $\mu$. The embedding is then applied to regular diffusions, and used to characterise the target laws for which a $H^p$-embedding may be found.<br />Comment: 22 pages, 4 figures
- Subjects :
- Statistics and Probability
Pure mathematics
Distribution (number theory)
Skorokhod problem
Stochastic process
Applied Mathematics
Probability (math.PR)
60G40, 60J60 (Primary) 60G44, 60J65 (Secondary)
Stopping time
Extension (predicate logic)
Combinatorics
Diffusion
Mathematics::Probability
Modelling and Simulation
Modeling and Simulation
FOS: Mathematics
Hp-embedding
Embedding
Brownian motion
Mathematics - Probability
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 03044149
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Stochastic Processes and their Applications
- Accession number :
- edsair.doi.dedup.....b58ee8c08400d77a5184b14526bc365d
- Full Text :
- https://doi.org/10.1016/j.spa.2004.01.003