欧勒 - 马鲁雅马方案的相对的收到随机微分方程与添加噪声
1School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan 250014, China.
Entropy (Basel, Switzerland)
|March 28, 2024
概括
这项研究分析了欧勒-马鲁雅马方案的随机微分方程的非对称行为,使用相对收率. 确定了总变化和加权变化距离的新趋同结果.
科学领域:
- 随机分析 随机分析
- 对SDEs的数值分析
背景情况:
- 欧勒-马鲁雅马方案是一个基本的数值方法,用于对随机微分方程 (SDEs) 的近似解决方案.
- 了解数值方案的收性质对于可靠的SDE模拟和分析至关重要.
- 欧勒-马鲁雅马方案的现有收率通常是强或弱的意义.
研究的目的:
- 为了研究由添加高斯噪声驱动的SDEs的欧勒-马鲁雅马方案的非对称行为.
- 以相对率来导出收率,补充现有的强和弱收结果.
- 为了建立新的收结果,总变化和加权变化距离.
主要方法:
- 对欧勒-马鲁雅马方案的相对中的收率的推导.
- 应用Pinsker不等式来推断总变化距离的收.
- 对具有 $\beta$-Hölder 连续漂移 (0 < $\beta$ < 1) 的 SDEs 的加权变化距离的趋同分析.
- 使用吉尔萨诺夫变换作为主要的数学工具.
主要成果:
- 确定了欧勒-马鲁雅马方案的相对的新收率.
- 由此衍生出的相对趋同补充了传统的强和弱率.
- 总变异距离的收通过Pinsker的不等式直接暗示.
- 对于具有 $\beta$-Hölder 连续漂移的情况,证明了加权变异距离的新趋同率.
结论:
- 这项研究提供了对欧勒-马鲁雅马方案的收性质的新见解,超出了标准的强和弱感.
- 相对的收率提供了一个有价值的替代测量方案的准确性.
- 总变化和加权变化距离的确定的收扩大了欧勒-马鲁雅马方案的适用性和理解,特别是对于非平滑漂移系数.
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