Brownian motions in the diffeomorphism group I
Compositio Mathematica, Volume 53 (1984) no. 1, p. 19-50
@article{CM_1984__53_1_19_0,
author = {Baxendale, Peter},
title = {Brownian motions in the diffeomorphism group I},
journal = {Compositio Mathematica},
publisher = {Martinus Nijhoff Publishers},
volume = {53},
number = {1},
year = {1984},
pages = {19-50},
zbl = {0547.58041},
mrnumber = {762306},
language = {en},
url = {http://www.numdam.org/item/CM_1984__53_1_19_0}
}

Baxendale, Peter. Brownian motions in the diffeomorphism group I. Compositio Mathematica, Volume 53 (1984) no. 1, pp. 19-50. http://www.numdam.org/item/CM_1984__53_1_19_0/

[1] R. Arens: Topologies for homeomorphism groups. Amer. J. Math. 68 (1946) 593-610. | MR 19916 | Zbl 0061.24306

[2] P. Baxendale: Gaussian measures on function spaces. Amer. J. Math. 98 (1976) 891-952. | MR 467809 | Zbl 0384.28011

[3] P. Baxendale: Wiener processes on manifolds of maps. Proc. Royal Soc. Edinburgh 87A (1980) 127-152. | MR 600452 | Zbl 0456.60074

[4] P. Baxendale: Stochastic flows and Malliavin calculus. Proc. 20th IEEE Conference on Decision and Control. New York: IEEE (1981) pp. 595-599. | Zbl 0503.60068

[5] E.B. Dynkin: Die Grundlagen der Theorie der Markoffshen Prozesse. Berlin: Springer (1961). | MR 131899 | Zbl 0091.13604

[6] K.D. Elworthy: Stochastic differential equations on manifolds. London Mathematical Society, Lecture Note Series 70. Cambridge: Cambridge University Press (1982). | MR 675100 | Zbl 0514.58001

[7] P. Feinsilver: Processes with independent increments on a Lie group. Trans. Amer. Math. Soc. 242 (1978) 73-121. | MR 483034 | Zbl 0403.60006

[8] J. Franks: Manifolds of Cr mappings and applications to differentiable dynamical systems. Advances in Mathematics Supplementary Series 4 (1979) 271-290. | MR 546811 | Zbl 0452.58013

[9] T.E. Harris: Brownian motions on the homeomorphisms of the plane. Ann. Probability 9 (1981) 232-254. | MR 606986 | Zbl 0457.60013

[10] G.A. Hunt: Semigroups of measures on Lie groups. Trans. Amer. Math. Soc. 81 (1956) 264-293. | Zbl 0073.12402

[11] N. Ikeda and S. Watanabe: Stochastic differential equations and diffusion processes. Amsterdam: North-Holland; Tokyo: Kodansha (1981). | MR 637061 | Zbl 0495.60005

[12] J.L. Kelley: General topology. Berlin: Springer (1955). | MR 370454

[13] H. Kunita: Stochastic differential equations and stochastic flows of homeomorphisms, Stochastic analysis and applications, to appear. | Zbl 0555.60039

[14] H.P. Mckean: Stochastic integrals. New York: Academic Press (1969). | MR 247684 | Zbl 0191.46603

[15] E. Nelson: An existence theorem for second order parabolic equations. Trans. Amer. Math. Soc. 88 (1958) 414-429. | MR 95341 | Zbl 0115.31101

[16] R.S. Palais: Foundations of global non-linear analysis. New York: Benjamin (1968). | MR 248880 | Zbl 0164.11102

[17] C.A. Rogers: Hausdorff measures. Cambridge: Cambridge University Press (1970). | MR 281862 | Zbl 0204.37601

[18] A.V. Skorohod: A note on Gaussian measures in Banach space. Theory Probab. Appl. 15 (1970) 519-520. | MR 277684 | Zbl 0218.28008

[19] D.W. Stroock and S.R.S. Varadhan: Limit theorems for random walks on Lie groups. Sankhyā Series A, 35 (1973) 277-294. | MR 517406 | Zbl 0299.60007

[20] D.W. Stroock and S.R.S. Varadhan: Multidimensional diffusion processes. Berlin: Springer (1979). | MR 532498 | Zbl 0426.60069

[21] D. WILLIAMS (ed.): Stochastic integrals (Proceedings, LMS Durham symposium, 1980), Lecture notes in mathematics 851. Berlin: Springer (1981). | MR 620983 | Zbl 0444.00014

[22] K. Yosida: Functional Analysis (6th edn.). Berlin: Springer (1980).