On strong comparison theorems for multidimensional stochastic differential equations

• Autorzy: Górski M.
• Języki publikacji: EN

Abstrakty

EN

In the paper we prove a strong comparison theorem for multidimensional Ito processes with respect to a local martingale. In the particular case of a Wiener process, a more general result is proved.

Słowa kluczowe

EN

multidimensional stochastic differential equations; strong comparison

PL

mocne twierdzenie; procesy stochastyczne; stochastyczne wielowymiarowe równania rózniczkowe; teoria prawdopodobieństwa

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1999
• Tom: Vol. 47, no 2
• Strony: 183--189
• Opis fizyczny: Bibliogr. 6 poz.,

Twórcy

autor

Górski M.

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Bibliografia

• [1] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland Publ. Co., Amsterdam Oxford New York; Kodanscha Ltd., Tokyo 1981.
• [2] T. Yamada, Y. Ogura, On the Strong Comparison Theorems for Solutions of SDE's, Zeitschrift für Wahr., 56(1) (1981) 3-19.
• [3] A. Milian, Stochastic viability and a comparison theorem, Colloquium Mathematicum, vol. LXVIII Fasc. 2 (1995).
• [4] C. Geiss, R. Manthey, Comparison Theorems for SDE's in finite and infinite dimensions, Stochastic Process. Appl., 53 (1994) 23-35.
• [5] S. Assing, R. Manthey, The behavior of solutions of stochastic differential inequalities, Prob. Th. Rel. Fields, 103 (1995) 493-514.
• [6] W. J. Anderson, Local behavior of solutions of stochastic differential equations, Trans. Amer. Math. Soc., 164 (1972) 309-320.