Paper Title:

On the Pathwise Uniqueness of Solutions to Stochastic Integral Equations of Ito Type

Author(s):

Romeo Negrea

Department of Mathematics,
Politehnica University of Timisoara,
P-ta Victoriei 2, 300006, Timisoara,
Romania.
E-mail: romeo.negrea@upt.ro

Abstract:

We give sufficient conditions for the pathwise uniqueness of solutions to nonlinear stochastic integral equations of Itô type. The result concerns a relaxation of the classical Lipschitz condition by allowing for a Nagumo-type fast-growing time dependence as the initial time is approached. We also propose a special subclass of functions N ⊂ M which shows that our considerations go beyond the classical contraction case. Moreover, they assure the facilities for to prove the existence and uniqueness of solutions and for the existence of the fixed points for some class of operators associated to stochastic integral equations.

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