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On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property

   
@article{EJP117,
	author = {Antoine Lejay},
	title = {On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {7},
	year = {2002},
	keywords = {stochastic differential equations, good sequence of semimartingales, conditions UT and UCV, Lévy area},
	abstract = {We study the limit of functionals of stochastic  processes for which an homogenization result holds.  All these functionals involve stochastic integrals.  Among them, we consider more particularly the Levy area  and those giving the solutions of some SDEs.  The main question is to know whether or not the  limit of the stochastic integrals is equal to the stochastic integral of the limit of  each of its terms. In fact, the answer  may be negative, especially in  presence of a highly oscillating first-order  differential term. This provides us some counterexamples to the theory of good sequence of semimartingales. 
},
	pages = {no. 18, 1-18},
	issn = {1083-6489},
	doi = {10.1214/EJP.v7-117},    
        url = {http://ejp.ejpecp.org/article/view/117}}