A generalized mean-reverting equation and applications

Nicolas Marie

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 799-828
  • ISSN: 1292-8100

Abstract

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Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the associated Itô map, and we provide an Lp-converging approximation with a rate of convergence (p ≫ 1). The regularity of the Itô map ensures a large deviation principle, and the existence of a density with respect to Lebesgue’s measure, for the solution of that generalized mean-reverting equation. Finally, we study a generalized mean-reverting pharmacokinetic model.

How to cite

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Marie, Nicolas. "A generalized mean-reverting equation and applications." ESAIM: Probability and Statistics 18 (2014): 799-828. <http://eudml.org/doc/273652>.

@article{Marie2014,
abstract = {Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T&gt; 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the associated Itô map, and we provide an Lp-converging approximation with a rate of convergence (p ≫ 1). The regularity of the Itô map ensures a large deviation principle, and the existence of a density with respect to Lebesgue’s measure, for the solution of that generalized mean-reverting equation. Finally, we study a generalized mean-reverting pharmacokinetic model.},
author = {Marie, Nicolas},
journal = {ESAIM: Probability and Statistics},
keywords = {stochastic differential equations; rough paths; large deviation principle; mean-reversion; gaussian processes; Gaussian processes},
language = {eng},
pages = {799-828},
publisher = {EDP-Sciences},
title = {A generalized mean-reverting equation and applications},
url = {http://eudml.org/doc/273652},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Marie, Nicolas
TI - A generalized mean-reverting equation and applications
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 799
EP - 828
AB - Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T&gt; 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the associated Itô map, and we provide an Lp-converging approximation with a rate of convergence (p ≫ 1). The regularity of the Itô map ensures a large deviation principle, and the existence of a density with respect to Lebesgue’s measure, for the solution of that generalized mean-reverting equation. Finally, we study a generalized mean-reverting pharmacokinetic model.
LA - eng
KW - stochastic differential equations; rough paths; large deviation principle; mean-reversion; gaussian processes; Gaussian processes
UR - http://eudml.org/doc/273652
ER -

References

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