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Density Estimates for the Solutions of Backward Stochastic Differential Equations Driven by Gaussian Processes
Xiliang Fan,
Jiang-lun Wu 
Potential Analysis, Volume: 54, Issue: 3, Pages: 483 - 501
Swansea University Author:
Jiang-lun Wu
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DOI (Published version): 10.1007/s11118-020-09835-7
Abstract
The aim of this paper is twofold. Firstly, we derive upper and lower non- Gaussian bounds for the densities of the marginal laws of the solutions to backward stochas- tic differential equations (BSDEs) driven by fractional Brownian motions. Our arguments consist of utilising a relationship between f...
| Published in: | Potential Analysis |
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| ISSN: | 0926-2601 1572-929X |
| Published: |
Springer Netherlands
Springer Science and Business Media LLC
2021
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa53408 |
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| Abstract: |
The aim of this paper is twofold. Firstly, we derive upper and lower non- Gaussian bounds for the densities of the marginal laws of the solutions to backward stochas- tic differential equations (BSDEs) driven by fractional Brownian motions. Our arguments consist of utilising a relationship between fractional BSDEs and quasilinear partial differ- ential equations of mixed type, together with the profound Nourdin-Viens formula. In the linear case, upper and lower Gaussian bounds for the densities and the tail probabilities of solutions are obtained with simple arguments by their explicit expressions in terms of the quasi-conditional expectation. Secondly, we are concerned with Gaussian estimates for the densities of a BSDE driven by a Gaussian process in the manner that the solution can be established via an auxiliary BSDE driven by a Brownian motion. Using the transfer theorem we succeed in deriving Gaussian estimates for the solutions. |
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| Keywords: |
Backward stochastic differential equations; Gaussian processes; fractional Brownian motion; density estimate; Malliavin calculus. |
| College: |
Professional Services |
| Issue: |
3 |
| Start Page: |
483 |
| End Page: |
501 |