Summary
We develop an Ito formula about a regular family of martingales in which we replace the parameter by a continuous semi-martingale. We give an application to an averaging problem, under mixing assumptions, in a stochastic differential equation with small parameter.
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Laboratoire de Probabilités, associé C.N.R.S., n∘ 224
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Sznitman, AS. Martingales dépendant d'un paramètre: une formule d'Ito. Z. Wahrscheinlichkeitstheorie verw Gebiete 60, 41–70 (1982). https://doi.org/10.1007/BF01957096
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DOI: https://doi.org/10.1007/BF01957096