|
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
MathSciNet review:
0356256
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
A.
A. Borovkov, Theorems on the convegence to Markov diffusion
processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
16 (1970), 47–76. MR 0285053
(44 #2277)
- 2.
Paul
R. Chernoff, Note on product formulas for operator semigroups,
J. Functional Analysis 2 (1968), 238–242. MR 0231238
(37 #6793)
- 3.
I.
I. Gihman and A.
V. Skorohod, Stokhasticheskie differentsialnye uravneniya,
Izdat. “Naukova Dumka”, Kiev, 1968 (Russian). MR 0263172
(41 #7777)
- 4.
Jerome
A. Goldstein, Some counterexamples involving selfadjoint
operators, Rocky Mountain J. Math. 2 (1972),
no. 1, 143–149. MR 0290163
(44 #7348)
- 5.
Thomas
G. Kurtz, Extensions of Trotter’s operator semigroup
approximation theorems, J. Functional Analysis 3
(1969), 354–375. MR 0242016
(39 #3351)
- 6.
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, 1968. MR
0247667 (40 #930)
- 7.
Walter
A. Rosenkrantz, Limit theorems for solutions to a class of
stochastic differential equations, Indiana Univ. Math. J.
24 (1974/75), 613–625. MR 0368143
(51 #4385)
- 8.
A.
V. Skorohod, Limit theorems for Markov processes, Teor.
Veroyatnost. i Primenen. 3 (1958), 217–264 (Russian,
with English summary). MR 0101560
(21 #370)
- 9.
Daniel
W. Stroock and S.
R. S. Varadhan, Diffusion processes with continuous coefficients.
II, Comm. Pure Appl. Math. 22 (1969), 479–530.
MR
0254923 (40 #8130)
- 10.
H.
F. Trotter, Approximation of semi-groups of operators, Pacific
J. Math. 8 (1958), 887–919. MR 0103420
(21 #2190)
- 11.
Kôsaku
Yosida, Functional analysis, Die Grundlehren der
Mathematischen Wissenschaften, Band 123, Academic Press Inc., New York,
1965. MR
0180824 (31 #5054)
- 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:
http://dx.doi.org/10.1090/S0002-9904-1974-13603-7
PII:
S 0002-9904(1974)13603-7
|
