Semimartingale Theory and Stochastic Calculus
Semimartingale Theory and Stochastic Calculus
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DOI：
10.1201/9780203739907
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
S. He;Chia-kang Wang;Jia-An Yan
中科院分区：
文献类型：
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作者：
S. He;Chia-kang Wang;Jia-An Yan
预赛。单调类定理。一致可积性。本质至上。条件期望的推广。解析集与Choquite容量。勒贝格-斯蒂尔杰斯积分。经典的鞅理论。基本的不平等。收敛定理。上鞅的分解定理。杜布的停止定理。具有连续时间的鞅。具有独立增量的进程。进程和停止时间。停止时代。循序渐进的可衡量、可选和可预测的进程。可预测和可访问的时代。有限变差过程。时不我待。THEROREMS组及其应用。截口定理。A.S.可预测时间的可预测性。完全无法进入的时代。完全的过滤和正常的条件。在鞅上的应用。流程的预测。可测量过程的预测。对增长过程的双重预测。停止时间和进程的应用程序。Doob-Meyer分解定理。离散类型的过滤。具有可积变差的鞅和平方可积鞅。具有可积变差的鞅。平方可积鞅的稳定子空间。纯不连续平方可积鞅的结构。二次变差。局部鞅。进程类的本地化。局部鞅的分解。局部鞅跳跃的刻画。半马丁氏和拟马丁氏。半鞅和特殊半鞅。拟鞅及其Rao分解。区间型随机集上的半鞅关于半鞅的收敛定理。随机积分。关于局部鞅的可预测过程的随机积分关于局部鞅的递进过程的补偿随机积分。可预测过程关于半鞅的随机积分。随机积分的Lenglart不等式和收敛定理。伊藤公式和Dolans-Dade指数公式。半鞅的地方时报。随机微分方程：Metivier-Pellaumail方法。鞅空间H1和BMO。H1-序和BMO-序。费弗曼不等式。H1的对偶空间。Davis不等式。Burkhold-Davis-Gundy不等式。令空间HR，p>；1.John-Nirenberg不等式。半乳糖属植物的特征。随机测量。半鞅的积分表示。利维进程。跳转进程。措施的变化。局部绝对连续性。格萨诺夫关于局部鞅和半鞅的定理。关于随机测度的Girsano定理。滤子约化下的半鞅与半鞅问题。半鞅的刻画。可预测的表示属性。强可预测表示属性。弱可预测表示属性。这两种可预测表示性质之间的关系。度量的绝对连续性和邻接性。度量的绝对连续性和邻接性。Hellinger过程。绝对连续性和邻接性的可预测标准。半鞅测度的绝对连续性和邻接性过程的弱收敛。D([O，8])和Skorokhod拓扑。Skorokhod拓扑下的连续性。测度的弱收敛。紧密性的标准。跳跃过程的弱收敛半群的弱收敛拟左连续半鞅弱收敛的条件。弱收敛于具有独立增量的拟左连续过程的条件弱收敛到布朗运动。其他应用和补充。
PRELIMINARIES. Monotone Class Theorems. Uniform Integrability. Essential Supremum. The Generalization of Conditional Expectation. Analytic Sets and Choquet Capacity. Lebesgue-Stieltjes Integrals. CLASSICAL MARTINGALE THEORY. Elementary Inequalities. Convergence Theorems. Decomposition Theorems for Supermartingales. Doob's Stopping Theorem. Martingales with Continuous Time. Processes with Independent Increments. PROCESSES AND STOPPING TIMES. Stopping Times. Progressive Measurable, Optional and Predictable Processes. Predictable and Accessible Times. Processes with Finite Variation. Changes of Time. SECTION THEROREMS AND THEIR APPLICATIONS. Section Theorems. A.s. Foretellability of Predicatable Times. Totally Inaccessible Times. Complete Filtrations and the Usual Conditions. Applications to Martingales. PROJECTIONS OF PROCESSES. Projections of Measurable Processes. Dual Projections of Increasing Processes. Applications to Stopping Times and Processes. Doob-Meyer Decomposition Theorem. Filtrations of Discrete Type. MARTINGALES WITH INTEGRABLE VARIATION AND SQUARE INTEGRABLE MARTINGALES. Martingales with Integrable Variation. Stable Subspaces of Square Integrable Martingales. The Structure of Purely Discontinuous Square Integrable Martingales. Quadratic Variation. LOCAL MARTINGALES. The Localization of Classes of Processes. The Decomposition of Local Martingales. The Characterization of Jumps of Local Martingales. SEMIMARTINGALES AND QUASIMARTINGALES. Semimartingales and Special Semimartingales. Quasimartingales and Their Rao Decompositions. Semimartingales on Stochastic Sets of Interval Type. Convergence Theorems for Semimartingales. STOCHASTIC INTEGRALS. Stochastic Integrals of Predictable Processes with Respect to Local Martingales. Compensated Stochastic Integrals of Progressive Processes with Respect to Local Martingales. Stochastic Integrals of Predictable Processes with Respect to Semimartingales. Lenglart's Inequality and Convergence Theorems for Stochastic Integrals. Ito's Formula and Doleans-Dade Exponential Formula. Local Times of Semimartingales. Stochastic Differential Equations: Metivier-Pellaumail Method. MARTINGALE SPACES H1 AND BMO. H1-Martingales and BMO-Martingales. Fefferman's Inequality. The Dual Space of H1. Davis Inequalities. Burkholder-Davis-Gundy Inequality. Martingale Spaces HR,p > 1. John-Nirenberg Inequality. THE CHARACTERISTICS OF SEMIMARTINGALES. Random Measures. The Integral Representation of Semimartingales. Levy Processes. Jump Processes. CHANGES OF MEASURES. Local Absolute Continuity. Girsanov's Theorems for Local Martingales and Semimartingales. Girsano's Theorems for Random Measures. Semimartingales under Reduction of Filtration and Semimartingale Problem. The Characterization of Semimartingales. PREDICTABLE REPRESENTATION PROPERTY. Strong Predictable Representation Property. Weak Predictable Representation Property. The Relation between the Two Kinds of Predictable Representation Properties. ABSOLUTE CONTINUITY AND CONTIGUITY OF MEASURES. Absolute Continuity and Contiguity of Measures. Hellinger Processes. Predictable Criteria for Absolute Continuity and Contiguity. Absolute Continuity and Contiguity of Semimartingale Measures. WEAK CONVERGENCE OF PROCESSES. D([O,8[) and the Skorokhod Topology. Continuity under the Skorokhod Topology. Weak Convergence of Measures. Criteria for Tightness. Weak Convergence of Jump Processes. WEAK CONVERGENCE OF SEMIMARTINGALES. The Conditions for Weak Convergence to a Quasi-Left-Continuous Semimartingale. The Conditions for Weak Convergence to a Quasi-Left-Continuous Process with Independent Increments. Weak Convergence to a Brownian Motion. Other Applications and Complements.