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Preliminaries to Probability Theory and Stochastic Differential Equations

In: Mathematical Methods in Robust Control of Linear Stochastic Systems

Author

Listed:
  • Vasile Dragan

    (Institute of Mathematics of the Romanian Academy)

  • Toader Morozan

    (Institute of Mathematics of the Romanian Academy)

  • Adrian-Mihail Stoica

    (University Politechnica of Bucharest)

Abstract

This first chapter collects 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. Classical results concerning the measure theory, integration, stochastic processes, and stochastic integrals are presented without proofs. Appropriate references are given; thus for the measure theory we mention [33, 55, 71, 75, 118, 138]; for the probability theory we refer to [32, 71, 119, 130, 138], and for the theory of stochastic processes and stochastic differential equations we cite [6, 18, 32, 71, 72, 85, 102, 105, 120, 121, 141, 152, 153]. However several results which can be found in some references less accessible are proved.

Suggested Citation

  • Vasile Dragan & Toader Morozan & Adrian-Mihail Stoica, 2013. "Preliminaries to Probability Theory and Stochastic Differential Equations," Springer Books, in: Mathematical Methods in Robust Control of Linear Stochastic Systems, edition 2, chapter 0, pages 1-38, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8663-3_1
    DOI: 10.1007/978-1-4614-8663-3_1
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