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Ito’s Lemma

In: Stochastic Processes and Calculus

Author

Listed:
  • Uwe Hassler

    (Goethe University Frankfurt)

Abstract

If a process is given as a stochastic Riemann and/or Ito integral, then one may wish to determine how a function of the process looks. This is achieved by Ito’s lemma as an ingredient of stochastic calculus. In particular, stochastic integrals can be determined and stochastic differential equations can be solved with it; we will get to know stochastic variants of familiar rules of differentiation (chain and product rule). For this purpose we approach Ito’s lemma step by step by first discussing it for Wiener processes, then by generalizing it for diffusion processes and finally by considering some extensions.

Suggested Citation

  • Uwe Hassler, 2016. "Ito’s Lemma," Springer Texts in Business and Economics, in: Stochastic Processes and Calculus, edition 1, chapter 11, pages 239-258, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-23428-1_11
    DOI: 10.1007/978-3-319-23428-1_11
    as

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