Summary
Solutions of systems of stochastic differential equations are shown to be stable in ℋp under ℋp perturbations of semimartingale differentials. Analogous results are obtained inp p when the solutions are not semimartingales but are only cadlag, adapted processes. Also, the solutions are shown to be stable under almost sure perturbations. These results are contrasted with the lack of stability under non-ℋp perturbations, a result originally obtained by Wong and Zakai.
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This research was supported in part by NSF Grant No. MCS77-00095
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Protter, P. ℋp stability of solutions of stochastic differential equations. Z. Wahrscheinlichkeitstheorie verw Gebiete 44, 337–352 (1978). https://doi.org/10.1007/BF01013196
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DOI: https://doi.org/10.1007/BF01013196