Anticipating stochastic calculus

  • David Nualart
Part of the Probability and its Applications book series (PIA)


As we have seen in Chapter 2, the Skorohod integral is an extension of the Itô integral that allows us to integrate stochastic processes that are not necessarily adapted to the Brownian motion. The adaptability assumption is replaced by some regularity condition. It is possible to develop a stochastic calculus for the Skorohod integral which is similar in some aspects to the classical Itô calculus. In this chapter we present the fundamental facts about this stochastic calculus, and we also discuss other approaches to the problem of constructing stochastic integrals for nonadapted processes (approximation by Riemann sums, development in a basis of L2 ([0,1]), substitution methods). The last section discusses noncausal stochastic differential equations formulated using anticipating stochastic integrals.


Brownian Motion Stochastic Differential Equation Continuous Version Stochastic Integral Stochastic Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • David Nualart
    • 1
  1. 1.Facultat de MatemàtiquesUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations