A convergent family of diffusion processes whose diffusion coefficients diverge
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- by Walter A. Rosenkrantz PDF
- Bull. Amer. Math. Soc. 80 (1974), 973-976
References
- A. A. Borovkov, Theorems on the convegence to Markov diffusion processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 16 (1970), 47–76. MR 285053, DOI 10.1007/BF00538767
- Paul R. Chernoff, Note on product formulas for operator semigroups, J. Functional Analysis 2 (1968), 238–242. MR 0231238, DOI 10.1016/0022-1236(68)90020-7
- I. I. Gihman and A. V. Skorohod, Stokhasticheskie differentsial′nye uravneniya, Izdat. “Naukova Dumka”, Kiev, 1968 (Russian). MR 0263172
- Jerome A. Goldstein, Some counterexamples involving selfadjoint operators, Rocky Mountain J. Math. 2 (1972), no. 1, 143–149. MR 290163, DOI 10.1216/RMJ-1972-2-1-143
- Thomas G. Kurtz, Extensions of Trotter’s operator semigroup approximation theorems, J. Functional Analysis 3 (1969), 354–375. MR 0242016, DOI 10.1016/0022-1236(69)90031-7
- Petr Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der mathematischen Wissenschaften, Band 151, Academia [Publishing House of the Czechoslovak Academy of Sciences], Prague; Springer-Verlag New York Inc., New York, 1968. MR 0247667
- Walter A. Rosenkrantz, Limit theorems for solutions to a class of stochastic differential equations, Indiana Univ. Math. J. 24 (1974/75), 613–625. MR 368143, DOI 10.1512/iumj.1975.24.24047
- A. V. Skorohod, Limit theorems for Markov processes, Teor. Veroyatnost. i Primenen. 3 (1958), 217–264 (Russian, with English summary). MR 0101560
- Daniel W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients. II, Comm. Pure Appl. Math. 22 (1969), 479–530. MR 254923, DOI 10.1002/cpa.3160220404
- H. F. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887–919. MR 103420, DOI 10.2140/pjm.1958.8.887
- Kôsaku Yosida, Functional analysis, Die Grundlehren der mathematischen Wissenschaften, Band 123, Academic Press, Inc., New York; Springer-Verlag, Berlin, 1965. MR 0180824
Additional Information
- Journal: Bull. Amer. Math. Soc. 80 (1974), 973-976
- MSC (1970): Primary 60F05, 60J60; Secondary 60J35, 60H10
- DOI: https://doi.org/10.1090/S0002-9904-1974-13603-7
- MathSciNet review: 0356256