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On multivalued stochastic integral equations driven by semimartingales

  • Marek T. Malinowski ORCID logo EMAIL logo
Published/Copyright: October 18, 2017
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Abstract

We consider multivalued stochastic integral equations driven by semimartingales. Such equations are formulated in two different forms, i.e., using multivalued stochastic up-trajectory and trajectory integrals, which are not equivalent. By the successive approximations method, we show the existence of a unique solution to each equation under a condition much weaker than the Lipschitz one. We indicate that the solutions are stable under small changes of the equation data. The results have immediate implications for solutions to single-valued stochastic integral equations driven by semimartingales.

Acknowledgements

The author would like to thank the anonymous referees for their remarks that led to the improvement of the paper.

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Received: 2015-01-30
Revised: 2015-10-19
Accepted: 2016-04-11
Published Online: 2017-10-18
Published in Print: 2019-09-01

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