|
Brownian motion, geometry, and generalizations of Picard's little theorem
Authors:
S. I. Goldberg and C. Mueller
Journal:
Bull. Amer. Math. Soc. 7 (1982), 259-263
MSC (1980):
Primary 32H25, 53C21, 60J65
MathSciNet review:
656207
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
Burgess
Davis, Picard’s theorem and Brownian
motion, Trans. Amer. Math. Soc. 213 (1975), 353–362. MR 0397900
(53 #1756), http://dx.doi.org/10.1090/S0002-9947-1975-0397900-8
- 2.
J.
Eells and L.
Lemaire, A report on harmonic maps, Bull. London Math. Soc.
10 (1978), no. 1, 1–68. MR 495450
(82b:58033), http://dx.doi.org/10.1112/blms/10.1.1
- 3.
R.
E. Greene and H.
Wu, Function theory on manifolds which possess a pole, Lecture
Notes in Mathematics, vol. 699, Springer, Berlin, 1979. MR 521983
(81a:53002)
- 4.
S.
I. Goldberg, T.
Ishihara, and N.
C. Petridis, Mappings of bounded dilatation of Riemannian
manifolds, J. Differential Geometry 10 (1975),
no. 4, 619–630. MR 0390964
(52 #11787)
- 5.
Samuel
I. Goldberg and Tôru
Ishihara, Harmonic quasiconformal mappings of Riemannian
manifolds, Amer. J. Math. 98 (1976), no. 1,
225–240. MR 0404698
(53 #8498)
- 6.
T.
E. Harris, The existence of stationary measures for certain Markov
processes, Proceedings of the Third Berkeley Symposium on Mathematical
Statistics and Probability, 1954–1955, vol. II, University of
California Press, Berkeley and Los Angeles, 1956, pp. 113–124.
MR
0084889 (18,941d)
- 7.
Wilfrid
S. Kendall, Brownian motion and a generalised
little Picard’s theorem, Trans. Amer.
Math. Soc. 275 (1983), no. 2, 751–760. MR 682729
(84c:58083), http://dx.doi.org/10.1090/S0002-9947-1983-0682729-8
- 8.
H.
P. McKean Jr., Stochastic integrals, Probability and
Mathematical Statistics, No. 5, Academic Press, New York, 1969. MR 0247684
(40 #947)
- 9.
Walter
Philipp, The central limit problem for mixing sequences of random
variables., Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
12 (1969), 155–171. MR 0246356
(39 #7660)
- 10.
Mark
A. Pinsky, Stochastic Riemannian geometry, Probabilistic
analysis and related topics, Vol. 1, Academic Press, New York, 1978,
pp. 199–236. MR 0501385
(58 #18752)
- 11.
Jean-Jacques
Prat, Étude asymptotique et convergence angulaire du
mouvement brownien sur une variété à courbure
négative, C. R. Acad. Sci. Paris Sér. A-B
280 (1975), no. 22, Aiii, A1539–A1542 (French,
with English summary). MR 0388557
(52 #9393)
- 12.
D. W. Strook and S. R. S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, Proc. 6th Berkeley Symp. on Math. Stat, and Prob. III (1970), 333-360.
- 1.
- B. Davis, Picard's theorem and Brownian motion, Trans. Amer. Math. Soc. 213 (1975), 353-362. MR 397900
- 2.
- J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68. MR 495450
- 3.
- R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Math., vol. 699, Springer-Verlag, Berlin, 1979. MR 521983
- 4.
- S. I. Goldberg, T. Ishihara and N. C. Petridis, Mappings of bounded dilatation of Riemannian manifolds, J. Differential Geom. 10 (1975), 619-630. MR 390964
- 5.
- S. I. Goldberg and T. Ishihara, Harmonic quasiconformal mappings of Riemannian manifolds, Amer. J. Math. 98 (1976), 225-240. MR 404698
- 6.
- T. E. Harris, The existence of stationary measures for certain Markov processes, Proc. of the 3rd Berkeley Symp. on Math. Stat. and Prob., Vol. II (1956), 113-124. MR 84889
- 7.
- W. S. Kendall, Brownian motion and a generalised little Picard 's theorem, Trans. Amer. Math. Soc. (to appear). MR 682729
- 8.
- H. P. McKean, Jr., Stochastic integrals, Academic Press, New York and London, 1969. MR 247684
- 9.
- W. Phillip, The central limit theorem for mixing sequences of random variables, Z. Wahrsch. Verv. Geb. 12 (1969), 155-171. MR 246356
- 10.
- M. Pinsky, Stochastic Riemannian geometry, Probabilistic Analysis and Related Topics, Vol. I (A. T. Barucha-Reid, ed.), Academic Press, New York, 1978. MR 501385
- 11.
- J.-J. Prat, Étude asymptotique et convergence angulaire du mouvement brownien sur une variété à courbure negative, C. R. Acad. Sci. Paris, Ser. A 280 (1975), 1539-1542. MR 388557
- 12.
- D. W. Strook and S. R. S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, Proc. 6th Berkeley Symp. on Math. Stat, and Prob. III (1970), 333-360.
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (1980):
32H25,
53C21,
60J65
Retrieve articles in all journals
with MSC (1980):
32H25,
53C21,
60J65
Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1982-15028-5
PII:
S 0273-0979(1982)15028-5
|
