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New inequalities of Gronwall type for the stochastic differential equations. (English) Zbl 1327.60116
Summary: In this paper, we establish some new nonlinear integral inequalities of Gronwall type for Itō integrals. These inequalities generalize some inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some stochastic differential equations. We will use this inequalities to show the existence and uniqueness of solutions for nonlinear EDS.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
54C60 Set-valued maps in general topology
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