TY  - JOUR
ID  - Alpay2013
LB  - Alpay2013
AU  - Alpay, Daniel
AU  - Kipnis, Alon
TI  - A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes
ST  - A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 3
SP  - 395
EP  - 417
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.3.395
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.3.395
AB  - 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.
KW  - stochastic integral
KW  - white noise space
KW  - fractional Brownian motion
SN  - 1232-9274
ER  -