Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations

In this article we provide conditions on the coefficient functions of the stochastic differential equation and on p ? (0, ?] that are sufficient for local Lipschitz continuity in the strong Lp-sense with respect to the initial value and we establish explicit estimates for the local Lipschitz continuity constants.

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