Existence, uniqueness, almost sure polynomial stability of solution to a class of highly nonlinear pantograph stochastic differential equations and the Euler-Maruyama approximation

@article{Milosevic2014ExistenceUA,
  title={Existence, uniqueness, almost sure polynomial stability of solution to a class of highly nonlinear pantograph stochastic differential equations and the Euler-Maruyama approximation},
  author={Marija Milosevic},
  journal={Applied Mathematics and Computation},
  year={2014},
  volume={237},
  pages={672-685}
}
In the first part of this paper the existence, uniqueness and almost sure polynomial stability of solutions for pantograph stochastic differential equations are considered, under nonlinear growth conditions. The results are obtained using the idea from (Mao and Rassias, 2005) [10], where stochastic differential equation with constant delay are considered. However, the presence of the unbounded delay in stochastic pantograph differential equations required certain modification of that idea… CONTINUE READING

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