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.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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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.
Erscheinungsjahr
Zeitschriftentitel
Stochastic Processes and their Applications
Band
64
Ausgabe
1
Seite(n)
31-38
ISSN
PUB-ID

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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. doi: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.