Density of the signature process of fBm
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- by Fabrice Baudoin, Qi Feng and Cheng Ouyang PDF
- Trans. Amer. Math. Soc. 373 (2020), 8583-8610 Request permission
Abstract:
We study the density of the signature of fractional Brownian motions with parameter $H>1/4$. In particular, we prove existence, smoothness, global Gaussian upper bounds, and Varadhan’s type asymptotics for this density. A key result is that the estimates on the density we obtain are controlled by the Carnot–Carathéodory distance of the group.References
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Additional Information
- Fabrice Baudoin
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 690937
- ORCID: 0000-0001-5645-1060
- Email: fabrice.baudoin@uconn.edu
- Qi Feng
- Affiliation: Department of Mathematics, University of Southern California, Los Angeles, California 90089
- ORCID: 0000-0001-8469-8650
- Email: qif@usc.edu
- Cheng Ouyang
- Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
- MR Author ID: 876636
- Email: couyang@math.uic.edu
- Received by editor(s): April 19, 2019
- Received by editor(s) in revised form: March 16, 2020
- Published electronically: September 29, 2020
- Additional Notes: The third author was supported in part by Simons grant #355480
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 8583-8610
- MSC (2010): Primary 60H10, 60D05, 58J65, 60H07
- DOI: https://doi.org/10.1090/tran/8165
- MathSciNet review: 4177269