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| EULER APPROXIMATION FOR NON-AUTONOMOUS MIXED STOCHASTIC DIFFERENTIAL EQUATIONS IN BESOV NORM |
| Sihui Yu,Weiguo Liu |
| (School of Statistics and Mathematics, Guangdong University of Finance $\&$ Economics, Guangzhou 510320, Guangdong, PR China) |
| DOI： |
| Abstract: |
| The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form
$$\big(r_{2}(t)((r_{1}(t)(y'(t))^{\alpha})')^{\beta}\big)'+q(t)y^{\gamma}\left(\sigma(t)\right)=0,\ \ \ t\geq t_{0}>0,$$
where $\int^{\infty}r_{1}^{-\frac{1}{\alpha}}(s)\text{d}s<\infty$ and $\int^{\infty}r_{2}^{-\frac{1}{\beta}}(s)\text{d}s<\infty$.
The criteria in this paper improve and complement some existing ones. The results are illustrated by two
Euler-type differential equations. |
| Key words: Brownian motion; fractional Brownian motion; Euler approximation; rate of convergence; Besov norm |