# AN EXISTENCE AND UNIQUENESS THEOREM OF STOCHASTIC DIFFERENTIAL EQUATIONS AND THE PROPERTIES OF THEIR SOLUTION

• BAE, MUN-JIN (Department of Mathematics, Changwon National University) ;
• PARK, CHAN-HO (Department of Mathematics, Changwon National University) ;
• KIM, YOUNG-HO (Department of Mathematics, Changwon National University)
• Accepted : 2019.09.08
• Published : 2019.09.30

#### Abstract

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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