Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]

Lyons TJ, Röckner M, Zhang TS (1996)
Stochastic Processes and their Applications 64(1): 31-38.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Lyons, TJ; Röckner, MichaelUniBi; Zhang, TS
Abstract / Bemerkung
We prove that for a given symmetric Dirichlet form of type E(u,upsilon) = integral(E)[A(z)del u(z), del upsilon(z)](H) mu(dz) with E = C-0[0, 1] and H = classical Cameron-Martin space the corresponding diffusion process (under P-mu) can be decomposed into a forward and a backward E-valued martingale. The construction of the martingale is direct and explicit since it is based on a modification of Levy's construction of Brownian motion. Applications to prove tightness of laws of diffusions of the above kind are given.
Stichworte
diffusions on Banach spaces; Dirichlet processes; Dirichlet forms; martingale decomposition
Erscheinungsjahr
1996
Zeitschriftentitel
Stochastic Processes and their Applications
Band
64
Ausgabe
1
Seite(n)
31-38
ISSN
0304-4149
Page URI
https://pub.uni-bielefeld.de/record/1638061

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Lyons TJ, Röckner M, Zhang TS. Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]. Stochastic Processes and their Applications. 1996;64(1):31-38.
Lyons, T. J., Röckner, M., & Zhang, T. S. (1996). Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]. Stochastic Processes and their Applications, 64(1), 31-38. https://doi.org/10.1016/S0304-4149(96)00078-6
Lyons, T. J., Röckner, M., and Zhang, T. S. (1996). Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]. Stochastic Processes and their Applications 64, 31-38.
Lyons, T.J., Röckner, M., & Zhang, T.S., 1996. Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]. Stochastic Processes and their Applications, 64(1), p 31-38.
T.J. Lyons, M. Röckner, and T.S. Zhang, “Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]”, Stochastic Processes and their Applications, vol. 64, 1996, pp. 31-38.
Lyons, T.J., Röckner, M., Zhang, T.S.: Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]. Stochastic Processes and their Applications. 64, 31-38 (1996).
Lyons, TJ, Röckner, Michael, and Zhang, TS. “Martingale decomposition of Dirichlet processes on the Banach space C-0[0,1]”. Stochastic Processes and their Applications 64.1 (1996): 31-38.

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