Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

A convergent family of diffusion processes whose diffusion coefficients diverge


Author: Walter A. Rosenkrantz
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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. A. Borovkov, Theorems on the convergence to Markov diffusion processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 16 (1970), 47-76. MR 44 #2277. MR 285053
  • 2. P. R. Chernoff, Note on product formulas for operator semigroups, J. Functional Analysis 2 (1968), 238-242. MR 37 #6793. MR 231238
  • 3. I. I. Gihman and A. V. Skorohod, Stochastic differential equations, "Naukova Dumka", Kiev, 1968; English transl., Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 72, Springer-Verlag, Berlin and New York, 1972. MR 41 #7777. MR 263172
  • 4. J. Goldstein, Some counterexamples involving selfadjoint operators, Rocky Mountain J. Math. 2 (1972), 143-149. MR 290163
  • 5. T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Functional Analysis 3 (1969), 354-375. MR 39 #3351. MR 242016
  • 6. P. Mandl, Analytical treatment of one-dimensional Markov processes, Die Grundlehren der math. Wissenschaften, Band 151, Academia, Prague; Springer-Verlag, New York, 1968. MR 40 #930. MR 247667
  • 7. W. Rosenkrantz, Limit theorems for solutions to a class of stochastic differential equations, Indiana Univ. Math. J. (to appear). MR 368143
  • 8. A. V. Skorohod, Limit theorems for Markov processes, Teor. Verojatnost. i Primenen. 3 (1958), 217-264=Theor. Probability Appl. 3 (1958), 202-246. MR 21 #370. MR 101560
  • 9. D. W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients. II, Comm. Pure Appl. Math. 22 (1969), 479-530. MR 40 #8130. MR 254923
  • 10. H. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887-919. MR 21 #2190. MR 103420
  • 11. K. Yosida, Functional analysis, Die Grundlehren der math. Wissenschaften, Band 123, Academic Press, New York; Springer-Verlag, Berlin, 1965. MR 31 #5054. MR 180824

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 60F05, 60J60, 60J35, 60H10

Retrieve articles in all journals with MSC (1970): 60F05, 60J60, 60J35, 60H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1974-13603-7

American Mathematical Society