Parameter estimation in stochastic differential equations
Parameter estimation in stochastic differential equations
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DOI：
10.1007/978-3-540-74448-1
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发表时间：
2007-09
期刊：
影响因子：
--
通讯作者：
J. Bishwal
中科院分区：
文献类型：
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作者：
J. Bishwal
随机微分方程和随机偏微分方程中的参数估计是一门模拟复杂现象并作出优美决策的科学、艺术和技术。这一课题吸引了来自多个数学领域以及其他相关领域（如经济学和金融学）的研究人员。本卷提出了基于连续和离散观测的相应连续模型中未知参数的估计，并广泛检查最大似然，最小对比和贝叶斯方法。由于目前高频数据的可用性，研究在观测时间长度大而观测时间间隔小的情况下几个估计量的精细渐近性质是有用的。此外，时空白噪声驱动的模型，对空间数据有用，以及更复杂的非马尔可夫和非半鞅模型，如模拟长记忆现象的分数扩散，在本卷中进行了检查。
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.