Measurable linear operators induced by stochastic processes

• Autorzy: Wiśniewski A.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to describe the structure of some class of measurable linear operators on the L2-space with the probability measure induced by a stochastic process with independent increments. Our results extends the similar fact that has been considered in [3] and [5] for measurable linear functionals.

Słowa kluczowe

EN

measurable linear operators; stochastic integrals

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 4
• Strony: 873--878
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Wiśniewski A.

• Institute of Mathematics, Szczecin University, ul. Wielkopolska 15, 70-451 Szczecin, Poland

Bibliografia

• [1] J. L. Doob, Stochastic Processes, John Wiley & Sons, New York and London, 1953.
• [2] M. Kanter, Random Linear Functionals and Why We Study Them, Lecture Notes in Math. vol. 645, Springer-Verlag, Berlin, Heidelberg, and New York, 1978, pp 114-123.
• [3] Nguen Chi Bao, On functionals induced by stochastic processes with independent increments, Bull, de l'Acad. Polon. des Sciences 23 (1975), 457-460.
• [4] A. V. Skorohod, Stochastic Processes with Independent Increments, Moscow, 1964 (in Russian).
• [5] K. Urbanik, Random linear functionals and random integrals, Colloq. Math. 33 (1975) 255-263.
• [6] K. Urbanik and W. A. Woyczyński, A random integral and Orlicz spaces, Bull. Acad. Polon. Sci. 15 (1967), 161-169.
• [7] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, vol. 1, 4th ed., Cambridge University Press, Cambridge, 1935.
• [8] A. Wiśniewski, Measurable linear operators on Banach spaces, Colloq. Math. 54 (1987), 261-265.
• [9] A. Wiśniewski, Measurable linear functionals and operators on Fréchet spaces, Proc Amer. Math. Soc. 114 (1992), 1079-1085.