Integrability and tail estimates for Gaussian rough differential equations

Thomas Cass; Christian Litterer; Terry Lyons

doi:10.1214/12-AOP821

Integrability and tail estimates for Gaussian rough differential equations

Thomas Cass^*, Christian Litterer, Terry Lyons

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameterH > 1/4. We remark on the relevance of such estimates to a number of significant open problems.

Original language	English
Pages (from-to)	3026-3050
Number of pages	25
Journal	Annals of Probability
Volume	41
Issue number	4
Early online date	3 Jul 2013
DOIs	https://doi.org/10.1214/12-AOP821
Publication status	Published - 20 Aug 2013

Keywords

Gaussian processes
Rough path analysis

Access to Document

10.1214/12-AOP821

Cite this

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title = "Integrability and tail estimates for Gaussian rough differential equations",

abstract = "We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameterH > 1/4. We remark on the relevance of such estimates to a number of significant open problems.",

keywords = "Gaussian processes, Rough path analysis",

author = "Thomas Cass and Christian Litterer and Terry Lyons",

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AU - Cass, Thomas

AU - Litterer, Christian

AU - Lyons, Terry

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AB - We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameterH > 1/4. We remark on the relevance of such estimates to a number of significant open problems.

KW - Gaussian processes

KW - Rough path analysis

U2 - 10.1214/12-AOP821

DO - 10.1214/12-AOP821

M3 - Article

AN - SCOPUS:84881537061

SN - 0091-1798

VL - 41

SP - 3026

EP - 3050

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -