Gaussian estimates for the solutions of some one-dimensional stochastic equations

Gaussian estimates for the solutions of some one-dimensional stochastic equations

Using covariance identities based on the Clark-Ocone representation formula we derive Gaussian density bounds and tail estimates for the probability law of the solutions of several types of stochastic differential equations, including Stratonovich equations with boundary condition and irregular drif...

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Main Authors: Nguyen, Tien Dung, Privault, Nicolas, Torrisi, Giovanni Luca
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2015
Subjects:
DRNTU::Science::Mathematics::Discrete mathematics
Online Access:https://hdl.handle.net/10356/79258
http://hdl.handle.net/10220/25437
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-792582023-02-28T19:28:22Z Gaussian estimates for the solutions of some one-dimensional stochastic equations Nguyen, Tien Dung Privault, Nicolas Torrisi, Giovanni Luca School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics Using covariance identities based on the Clark-Ocone representation formula we derive Gaussian density bounds and tail estimates for the probability law of the solutions of several types of stochastic differential equations, including Stratonovich equations with boundary condition and irregular drifts, and equations driven by fractional Brownian motion. Our arguments are generally simpler than the existing ones in the literature as our approach avoids the use of the inverse of the Ornstein-Uhlenbeck operator. Accepted version 2015-04-22T03:49:08Z 2019-12-06T13:21:00Z 2015-04-22T03:49:08Z 2019-12-06T13:21:00Z 2015 2015 Journal Article Nguyen, T. D., Privault, N., & Torrisi, G. L. (2015). Gaussian estimates for the solutions of some one-dimensional stochastic equations. Potential analysis, 43(2), 289-311. https://hdl.handle.net/10356/79258 http://hdl.handle.net/10220/25437 10.1007/s11118-015-9472-7 en Potential analysis © 2015 Springer Science+Business Media Dordrecht. This is the author created version of a work that has been peer reviewed and accepted for publication by Potential Analysis, Springer Science+Business Media Dordrecht. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [Article DOI: http://dx.doi.org/10.1007/s11118-015-9472-7]. 28 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Discrete mathematics
spellingShingle DRNTU::Science::Mathematics::Discrete mathematics
Nguyen, Tien Dung
Privault, Nicolas
Torrisi, Giovanni Luca
Gaussian estimates for the solutions of some one-dimensional stochastic equations
description Using covariance identities based on the Clark-Ocone representation formula we derive Gaussian density bounds and tail estimates for the probability law of the solutions of several types of stochastic differential equations, including Stratonovich equations with boundary condition and irregular drifts, and equations driven by fractional Brownian motion. Our arguments are generally simpler than the existing ones in the literature as our approach avoids the use of the inverse of the Ornstein-Uhlenbeck operator.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Nguyen, Tien Dung
Privault, Nicolas
Torrisi, Giovanni Luca
format Article
author Nguyen, Tien Dung
Privault, Nicolas
Torrisi, Giovanni Luca
author_sort Nguyen, Tien Dung
title Gaussian estimates for the solutions of some one-dimensional stochastic equations
title_short Gaussian estimates for the solutions of some one-dimensional stochastic equations
title_full Gaussian estimates for the solutions of some one-dimensional stochastic equations
title_fullStr Gaussian estimates for the solutions of some one-dimensional stochastic equations
title_full_unstemmed Gaussian estimates for the solutions of some one-dimensional stochastic equations
title_sort gaussian estimates for the solutions of some one-dimensional stochastic equations
publishDate 2015
url https://hdl.handle.net/10356/79258
http://hdl.handle.net/10220/25437
_version_ 1759858416166109184

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