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On the power series representation of smooth conformal martingales

Published online by Cambridge University Press:  22 January 2016

Nguyen Xuan-loc
Nguyen Xuan-loc*
Affiliation:
Department of Mathematical Statistics, Institute of Computer Science and Cibernetics, Lieu Giai Ba Dinh, Ha Not R. S. Viet Nam
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We introduce here the notion of (stochastically) differentiable process with respect to a fixed conformal martingale and compute the remainder term of the Taylor expansion of the given process (Definition 1 and Proposition 3). An a-priori estimate in the L2-norm of the above mentioned remainder term is given and consequently a power series representation of smooth conformal martingales is obtained (Theorem 4).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 103 , October 1986 , pp. 15 - 27
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[1] Fuglede, B., Fine topology and finely holomorphic functions, Proc. 18th. Scandinavian Cong, of Mathematicians, Birkhäuser, (1981).Google Scholar
[2] Getoor, R. K. and Sharpe, M. J., Conformal martingales, Invent. Math., 16 (1972), 271–308.Google Scholar
[3] Nguyen-Xuan-Loc, , Singularities of locally analytic processes, Proc. Symp. on Potential Theory, Lect. Notes in Math., No. 787, Springer-Verlag (1980), 267–288.Google Scholar
[4] Caroli, R. and Walsh, J. B., Stochastic integrals in the plane, Acta. Math., 134 (1975), 111–183.Google Scholar
[5] Yor, M., Etude de certains processus (stochastiqument) differentiables ou holomorphes, Ann. Inst. Henri Poincaré, XIII, No. 1 (1977), 1–25.Google Scholar
[6] Debiard, et Gaveau, B., Potentiel fin et algebre de fonctions analytiques, J. Funct. Anal., 16 (1974), 289–304.Google Scholar
[7] Walsh, J. B., A property of conformal martingales, Seminaire de Probabilities 11, Lect. Notes in Math., No. 581, Springer-Verlag (1975/76), 490–492.Google Scholar