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This first chapter collects in its first part, for the readers convenience, some definitions and fundamental results concerning the measure theory and the stochastic processes theory which are needed in the following developments of the book. All the presented results will be given without proof, such results being classical, and appropriate references will be added for the interested readers. The second part of the chapter is devoted to the presentation of the different types of stochastic differential equations with jumps that will be studied in the rest of the book. Fundamental existence and unicity results of the solutions of such equations will be also stated and proved (Propositions 1.1, 1.2 and 1.3).

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Preliminaries to Probability Theory and Jump Stochastic Linear Differential Equations

  • 章节

  • 发表日期：

    2025年

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  • Vasile Drăgan,
  • Samir Aberkane,
  • Ioan Lucian Popa

摘要

This first chapter collects in its first part, for the readers convenience, some definitions and fundamental results concerning the measure theory and the stochastic processes theory which are needed in the following developments of the book. All the presented results will be given without proof, such results being classical, and appropriate references will be added for the interested readers. The second part of the chapter is devoted to the presentation of the different types of stochastic differential equations with jumps that will be studied in the rest of the book. Fundamental existence and unicity results of the solutions of such equations will be also stated and proved (Propositions 1.1, 1.2 and 1.3).