On solutions of stochastic integral equations

• Autorzy: Malczak J. , Wędrychowicz S.
• Języki publikacji: EN

Abstrakty

EN

We deal with the stochastic integral equation [formula]. Sufficient conditions for the existence and uniqueness of random solution and its asymptotic behaviour are given. We use the Banach space of tempered functions which contains the space D(([0,+ ])and we apply the Banach fixed point principle.

Słowa kluczowe

EN

stochastic integral equation

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2002
• Tom: [Z] 42(1)
• Strony: 75--85
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Malczak J.

• Zakład Matematyki Stosowanej, Wyższa Szkoła Biznesu-NLU, ul. Zielona 27, 33-300 Nowy Sącz, Polska

autor

Wędrychowicz S.

• Katedra Matematyki, Politechnika Rzeszowska, ul. W. Pola 2, 35-959 Rzeszów, Polska

Bibliografia

• [1] J. Banaś, D. Szynal and S. Wedrychowicz, (1991), On existence, asymptotic behaviour and stability of solutions of stochastic integral equations, Stochastic Analysis and Appl. 9 (4) (1991), 363-385.
• [2] C. Doleans-Dade, On the existence and unicity of solution of stochastic integral equation, Z. Warsch. Verw. Geb. 36 (1976) 93-101.
• [3] C. Doleans-Dade and P. A. Meyer, Equations Différentialles Stochastiques, Seminaire de Probabilities XI, Lecture Notes Mathematics 581 (1977), Springer-Verlag, Berlin, 376-382.
• [4] R. J. Elliott, Stochastic Calculus and Applications, New York, Heidelberg Berlin, Springer-Verlag, 1982.
• [5] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion process, Oxford, New York, Amsterdam, North-Holland Publishing Company, 1981.
• [6] P. E. Protter, On the existence, uniqueness convergence explosions of solution of systems of stochastic integral equations, Ann. Prob. 5 (1977), 243-261.
• [7] R. Subramanian and K. Balachandran, (1997) Existence of solutions of general nonlinear stochastic integral equations, Indian J. Pure Appl. Math. 28 (6) (1997), 75-789.
• [8] R. Subramanian and K. Balachandran, Existence of solution of a class of stochastic Volterra integral equations with applications to chemotherapy, J. Austral. Math. Soc. Ser. B. 41 (1999), 93-104.
• [9] D. Szynal and S. Wędrychowicz, On solutions of a stochastic integral equation of the Volterra type with applications for chemotherapy, J. Appl. Prob. 25 (1988), 257-267.
• [10] D. Szynal and S. Wędrychowicz, On solutions of some nonlinear stochastic integral equation, Yokohama Math. J. Vol. 41 (1993), 31-37.