On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property
Antoine Lejay, INRIA Lorraine
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.
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