On weak convergence of one-dimensional diffusions with time-dependent coefficients

• Autorzy: Rozkosz Andrzej
• Języki publikacji: EN

Abstrakty

EN

We investigate stability, with respect to convergence of coefficients, of one-dimensional Itô diffussions as well as one-dimensional diffusions corresponding to second order divergence form operators. We assume that the coefficients are measurable, uniformly bounded and that the diffusion coefficients are uniformly positive.

Słowa kluczowe

EN

Itô diffussion; stability; convergence

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 1
• Strony: 101--117
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Rozkosz Andrzej

• Faculty of Mathematics and Informatics, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] L. A. Alyushina and N. V. Krylov, Passage to the limit in ltd stochastic equations, Theory Probab. Appl. 33 (1988), pp. 1-10.
• [2] F. Colombini and S. Spagnolo, Sur la convergence de solutions d’équations paraboliques, J. Math. Pures Appl. 56 (1977), pp. 205-263.
• [3] S. N. Kruzkov, Nonlinear parabolic equations with two independent variables (in Russian), Trudy Moskov. Mat. Obsc. 16 (1967), pp. 329-346.
• [4] N. V. Krylov, Controlled Diffusion Processes, Springer, New York 1980.
• [5] O. A. Ladyżenskaja, V. A. Solonnikov and N. N. Ural’ceva, Linear and Quasi-linear Equations of Parabolic type, Transí. Math. Monographs 23, Amer. Math. Soc., Providence, R. I., 1968.
• [6] V. G, Markov and O. A. Oleinik, On propagation of heat in one-dimensional disperse media, J. Appl. Math. Mech. 39 (1975), pp. 1028-1037.
• [7] A. Rozkosz, Weak convergence of diffusions corresponding to divergence form operators, Stochastics Stochastics Rep. 57 (1996), pp. 129-157.
• [8] — and L. Słomiński, On weak convergence of solutions of one-dimensional stochastic differential equations, ibidem 31 (1990), pp. 27-54.
• [9] S. Spagnolo, Convergence of parabolic equations, Boll. Un. Mat. Ital. 14-В (1977), pp. 547-568.
• [10] D. W. Stroock, Diffusion semigroups corresponding to uniformly elliptic divergence form operators, in: Séminaire de Probabilités XXII, J. Azéma, P. A. Meyer and M. Yor (Eds.), Lecture Notes in Math. 1321, Springer, Berlin 1988, pp. 316-347.
• [11] — and S. R. S. Varadhan, Diffusion processes, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 3, Univ. California Press, Berkeley, Calif., 1972, pp. 361-368.
• [12] — Multidimensional Diffusion Processes, Springer, New-York 1979.
• [13] V. У. Zhikov, S. M. Kozlov and O. A. Oleinik, G-convergence of parabolic operators, Russian Math. Surveys 36, No. 1 (1981), pp. 9-60.
• [14] — and Kha T’en Ngoan, Averaging and G-convergence of differential operators, ibidem 34, No. 5 (1979), pp. 69-147.