Browsing by Subject "stochastic integral"

Now showing 1 - 5 of 5

Access status: Open Access ,
A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes
(2013) Alpay, Daniel; Kipnis, Alon
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.
Access status: Restricted ,
Kredyty pod zastaw akcyjny
(Data obrony: 2017-10-23) Lorens, Marta
Wydział Matematyki Stosowanej
Access status: Restricted ,
Strategie zabezpieczające na rynkach z arbitrażem
(Data obrony: 2018-06-20) Wolszczak, Wioletta
Wydział Matematyki Stosowanej
Access status: Restricted ,
Teoria portfela z wykorzystaniem benchmarkingu
(Data obrony: 2012-11-19) Balon, Kinga
Wydział Matematyki Stosowanej
Access status: Open Access ,
White noise based stochastic calculus associated with a class of Gaussian processes
(2012) Alpay, Daniel; Attia, Haim; Levanony, David
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.