On pathwise stochastic integration with respect to semimartingales

• Autorzy: Łochowski R. M.
• Języki publikacji: EN

Abstrakty

EN

For any real-valued stochastic process X with càdlàg paths we define non-empty family of processes which have locally finite total variation, have jumps of the same order as the process X and uniformly approximate its paths on compacts. The application of the defined class is the definition of stochastic integral with semimartingale integrand and integrator as a limit of pathwise Lebesgue-Stieltjes integrals. This construction leads to the stochastic integral with some correction term (different from the Stratonovich integral). Using properties of a functional called truncated variation we compare the obtained result with classical results of Wong-Zakai and Bichteler on pathwise stochastic integration.

Słowa kluczowe

EN

stochastic integral; truncated variation; double Skorokhod map

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2014
• Tom: Vol. 34, Fasc. 1
• Strony: 23--43
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Łochowski R. M.

• Warsaw School of Economics, ul. Madalińskiego 6/8, 02-513 Warszawa, Poland
• Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).