Paper Title:

Derivation of the Existence Theorem of the Solution of the Stochastic Functional Differential Equation Using Conditions Given Partial Weights

Author(s):

Young-Ho Kim

Department of Mathematics,
Changwon National University
Changwon, Gyeongsangnam 51140,
Korea.
E-mail: yhkim@changwon.ac.kr

Abstract:

The main purpose of this note was to demonstrate the solution existence theorem for stochastic functional differential equations under sufficient conditions. As an alternative to the stochastic process theory of the stochastic functional differential equations, we impose a partial weighting condition and a weakened linear growth condition. We first show that the condition guarantees existence and uniqueness and then show some exponential estimates for the solution.

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