英文标题：
《On parameter identification in stochastic differential equations by
penalized maximum likelihood》
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作者：
Fabian Dunker and Thorsten Hohage
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最新提交年份：
2014
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英文摘要：
In this paper we present nonparametric estimators for coefficients in stochastic differential equation if the data are described by independent, identically distributed random variables. The problem is formulated as a nonlinear ill-posed operator equation with a deterministic forward operator described by the Fokker-Planck equation. We derive convergence rates of the risk for penalized maximum likelihood estimators with convex penalty terms and for Newton-type methods. The assumptions of our general convergence results are verified for estimation of the drift coefficient. The advantages of log-likelihood compared to quadratic data fidelity terms are demonstrated in Monte-Carlo simulations.
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中文摘要：
在本文中，我们给出了随机微分方程系数的非参数估计，如果数据由独立的、同分布的随机变量描述。该问题被描述为一个非线性不适定算子方程，其确定性正演算子由福克-普朗克方程描述。我们推导了带有凸惩罚项的惩罚极大似然估计和牛顿型方法的风险收敛速度。对于漂移系数的估计，我们的一般收敛结果的假设得到了验证。与二次数据保真度项相比，对数似然项的优势在蒙特卡罗模拟中得到了证明。
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分类信息：

一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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