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Riemann Integrals

In: Stochastic Processes and Calculus

Author

Listed:
  • Uwe Hassler

    (Goethe University Frankfurt)

Abstract

In this chapter we deal with stochastic Riemann integrals, i.e. with ordinary Riemann integrals with a stochastic process as the integrand. Mathematically, these constructs are relatively unsophisticated, they can be defined pathwise for continuous functions as in conventional (deterministic) calculus. However, this pathwise definition will not be possible any longer for e.g. Ito integrals in the chapter after next. Hence, at this point we propose a way of defining integrals as a limit (in mean square) which will be useful later on. If the stochastic integrand is in particular a Wiener process, then the Riemann integral follows a Gaussian distribution with zero expectation and the familiar formula for the variance. A number of examples will facilitate the understanding of this chapter.

Suggested Citation

  • Uwe Hassler, 2016. "Riemann Integrals," Springer Texts in Business and Economics, in: Stochastic Processes and Calculus, edition 1, chapter 8, pages 179-197, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-23428-1_8
    DOI: 10.1007/978-3-319-23428-1_8
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