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An Itô calculus for a class of limit processes arising from random walks on the complex plane

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  • Bonaccorsi, Stefano
  • Calcaterra, Craig
  • Mazzucchi, Sonia

Abstract

Within the framework of the previous paper (Bonaccorsi and Mazzucchi, 2015), we develop a generalized stochastic calculus for processes associated to higher order diffusion operators. Applications to the study of a Cauchy problem, a Feynman–Kac formula and a representation formula for higher derivatives of analytic functions are also given.

Suggested Citation

  • Bonaccorsi, Stefano & Calcaterra, Craig & Mazzucchi, Sonia, 2017. "An Itô calculus for a class of limit processes arising from random walks on the complex plane," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2816-2840.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:9:p:2816-2840
    DOI: 10.1016/j.spa.2016.12.009
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    References listed on IDEAS

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    1. Hochberg, Kenneth J. & Orsingher, Enzo, 1994. "The arc-sine law and its analogs for processes governed by signed and complex measures," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 273-292, August.
    2. Bonaccorsi, Stefano & Mazzucchi, Sonia, 2015. "High order heat-type equations and random walks on the complex plane," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 797-818.
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