Opuscula Math. 33, no. 3 (2013), 395-417
http://dx.doi.org/10.7494/OpMath.2013.33.3.395

 
Opuscula Mathematica

A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes

Daniel Alpay
Alon Kipnis

Abstract. Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida's white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.

Keywords: stochastic integral, white noise space, fractional Brownian motion.

Mathematics Subject Classification: 60H40, 60H05.

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  • Daniel Alpay
  • Ben Gurion University of the Negev, Department of Mathematics, P.O.B. 653, Be'er Sheva 84105, Israel
  • Alon Kipnis
  • Ben Gurion University of the Negev, Department of Electrical Engineering, P.O.B. 653, Be'er Sheva 84105, Israel
  • Received: 2012-08-18.
  • Revised: 2012-12-16.
  • Accepted: 2012-12-16.
Opuscula Mathematica - cover

Cite this article as:
Daniel Alpay, Alon Kipnis, A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes, Opuscula Math. 33, no. 3 (2013), 395-417, http://dx.doi.org/10.7494/OpMath.2013.33.3.395

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