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An Introduction to Stochastic Differential Equations

In: Almost Periodic Stochastic Processes

Author

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  • Paul H. Bezandry

    (Howard University, Department of Mathematics)

  • Toka Diagana

    (Howard University, Department of Mathematics)

Abstract

Chapter 3 develops probabilistic tools needed for the analysis of stochastic problems in the book. It begins with the review of the fundamentals of probability including the notion of conditional expectation, which is very useful in the sequel. This chapter also offers an introduction to the mathematical theory of stochastic processes, including the notion of continuity, measurability, stopping times, martingales,Wiener processes, and Gaussian processes. These concepts enable us to define the so-called Itô integral, the Itô formula, and diffusion processes. An extension of Itô integrals to Hilbert spaces and stochastic convolution integrals are also discussed. An investigation on stochastic differential equations driven by Wiener processes is given at end of the chapter. Special emphasis will be on the boundedness and stability of solutions.

Suggested Citation

  • Paul H. Bezandry & Toka Diagana, 2011. "An Introduction to Stochastic Differential Equations," Springer Books, in: Almost Periodic Stochastic Processes, chapter 0, pages 61-115, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-9476-9_3
    DOI: 10.1007/978-1-4419-9476-9_3
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