Abstract
Given a stochastic differential equation of which coefficients satisfy Yamada–Watanabe condition or Nakao-Le Gall condition. We prove that its strong solution can be constructed on any probability space using a priori estimates and also using Ito theory based on Picard’s approximation scheme.
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Acknowledgements
This work is motivated by stimulating discussions with Toshio Yamada. Also, we received valuable comments from Tomoyuki Ichiba. The author would like to thank them very much. Finally, we are grateful to the anonymous referee who made significant suggestions.
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Okumura, T. (2019). On a Construction of Strong Solutions for Stochastic Differential Equations with Non-Lipschitz Coefficients: A Priori Estimates Approach. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités L. Lecture Notes in Mathematics(), vol 2252. Springer, Cham. https://doi.org/10.1007/978-3-030-28535-7_10
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DOI: https://doi.org/10.1007/978-3-030-28535-7_10
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