Abstract
We prove the existence and unicity of a strong solution for the stochastic differential equation dXt=a(X,t)dt, where a is "predictable", locally bounded and locally lipschitzian and X is a semi-martingale (cf. [3]). The pro of uses an inequality for such a semi-martingale which is established in the paragraph B. There results have been shown in [2] and generalize [1].
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References
C. Doleans-Dade: On the existence and unicity of stochastic integral equations.
M. Metivier et J. Pellaumail: Inégalites pour une martingale et équations différentielles stochastiques. Séminaire de Rennes 1977 (to appear).
P.A. Meyer: Séminaire de probabilités X, Springer-Verlag 1976.
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© 1978 Springer-Verlag
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Pellaumail, J. (1978). An inequality for the semi-martingales application to stochastic differential equations. In: Weron, A. (eds) Probability Theory on Vector Spaces. Lecture Notes in Mathematics, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068820
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DOI: https://doi.org/10.1007/BFb0068820
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