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This chapter provides an overview of optionality and predictability, general stopping times, processes of finite variations, optional martingales and semimartingales, along with their integration with respect to random measures. The chapter is ended by the canonical decomposition of optional semimartingales and the change of variables formulas (see Abdelghani and Melnikov, Optional pRocesses: theory and applications, 2020; Gal’chuk, Theory Probab Appl 29(1):483–521, 1980; Horowitz, Probab Theory Related Fields 43(3):263–272, 1978; Lenglart, Tribus de Meyer et théorie des processus, 1980; Lepingle, Sur la représentation des sauts des martingales, 1977; Dellacherie and Meyer, Un nouveau théorème de projection et de section, 1975, and Kühn et al., Electron Commun Probab 14:192–201, 2009).

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Basic Elements of Optional Stochastic Analysis

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  • 发表日期：

    2026年

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  • Alexander Melnikov

摘要

This chapter provides an overview of optionality and predictability, general stopping times, processes of finite variations, optional martingales and semimartingales, along with their integration with respect to random measures. The chapter is ended by the canonical decomposition of optional semimartingales and the change of variables formulas (see Abdelghani and Melnikov, Optional pRocesses: theory and applications, 2020; Gal’chuk, Theory Probab Appl 29(1):483–521, 1980; Horowitz, Probab Theory Related Fields 43(3):263–272, 1978; Lenglart, Tribus de Meyer et théorie des processus, 1980; Lepingle, Sur la représentation des sauts des martingales, 1977; Dellacherie and Meyer, Un nouveau théorème de projection et de section, 1975, and Kühn et al., Electron Commun Probab 14:192–201, 2009).