# Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations

ESAIM: Probability and Statistics (2010)

- Volume: 9, page 165-184
- ISSN: 1292-8100

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topMarty, Renaud. "Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations." ESAIM: Probability and Statistics 9 (2010): 165-184. <http://eudml.org/doc/104328>.

@article{Marty2010,

abstract = {
We consider a differential equation with a random rapidly varying coefficient.
The random coefficient is a
Gaussian process with slowly decaying correlations and compete with a periodic component. In the
asymptotic framework corresponding to the separation of scales present in the
problem, we prove that the solution of the differential equation
converges in distribution to the solution of a stochastic differential equation
driven by a classical Brownian motion in some cases, by a fractional Brownian
motion in other cases. The proofs of these results are based on the Lyons theory of
rough paths. Finally we discuss applications in two physical situations.
},

author = {Marty, Renaud},

journal = {ESAIM: Probability and Statistics},

keywords = {Limit theorems; stationary processes; rough paths.; rough paths},

language = {eng},

month = {3},

pages = {165-184},

publisher = {EDP Sciences},

title = {Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations},

url = {http://eudml.org/doc/104328},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Marty, Renaud

TI - Asymptotic behavior of differential equations driven by periodic and random processes with slowly decaying correlations

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 165

EP - 184

AB -
We consider a differential equation with a random rapidly varying coefficient.
The random coefficient is a
Gaussian process with slowly decaying correlations and compete with a periodic component. In the
asymptotic framework corresponding to the separation of scales present in the
problem, we prove that the solution of the differential equation
converges in distribution to the solution of a stochastic differential equation
driven by a classical Brownian motion in some cases, by a fractional Brownian
motion in other cases. The proofs of these results are based on the Lyons theory of
rough paths. Finally we discuss applications in two physical situations.

LA - eng

KW - Limit theorems; stationary processes; rough paths.; rough paths

UR - http://eudml.org/doc/104328

ER -

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