Imperial College London
Portrait Picture

Professor Xue-Mei Li

Faculty of Natural Sciences, Department of Mathematics

Chair in Probability and Stochastic Analysis
 
 
 
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Contact

 

+44 (0)20 7594 3709xue-mei.li Website CV

 
 
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Location

 

6M51Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Gehringer:2021,
author = {Gehringer, J and Li, X-M and Sieber, J},
publisher = {arXiv},
title = {Functional limit theorems for volterra processes and applications tohomogenization},
url = {http://arxiv.org/abs/2104.06364v1},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - We prove an enhanced limit theorem for additive functionals of amultidimensional Volterra process $(y_t)_{t\geq 0}$. As an application, weestablish weak convergence of the solutions of rough differential equations(RDE) of the form $$  dx^\varepsilon_t=\frac 1 {\sqrt \varepsilon}f(x_t^\varepsilon,y_{\frac{t}{\varepsilon}})\,dt+g(x_t^\varepsilon)\,d\mathbf{B}_t,$$and identify their limits as solutions of an RDE driven by a Gaussian fieldwith a drift coming from the L\'evy area correction of the limiting roughdriver. The equation models a passive tracer in a random field.  In particular if $h$ is random field such that $h(x, \cdot)$ asemi-martingale with spatial parameter $x$, we show that the solutions of theequations $$ dx^\varepsilon_t=\frac 1 {\sqrt \epsilon}f(x_t^\varepsilon,y_{\frac{t}{\varepsilon}})\,dt+h(x_t^\varepsilon, dt),$$  converge weakly to that of a Kunita type It\^o SDE $dx_t=G(x_t,dt)$ where$G(x,t)$ is a semi-martingale with spatial parameters. Furthermore the$N$-point motions converge.
AU  - Gehringer,J
AU  - Li,X-M
AU  - Sieber,J
PB  - arXiv
PY  - 2021///
TI  - Functional limit theorems for volterra processes and applications tohomogenization
UR  - http://arxiv.org/abs/2104.06364v1
UR  - http://hdl.handle.net/10044/1/88950
ER  -
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