# Spectral representation of isotropic random currents

Séminaire de probabilités de Strasbourg (1989)

- Volume: 23, page 503-526

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topWong, Eugene, and Zakai, Moshe. "Spectral representation of isotropic random currents." Séminaire de probabilités de Strasbourg 23 (1989): 503-526. <http://eudml.org/doc/113698>.

@article{Wong1989,

author = {Wong, Eugene, Zakai, Moshe},

journal = {Séminaire de probabilités de Strasbourg},

keywords = {isotropic random currents; homogeneity; isotropy; Ito's characterization of the spectral measure; spectral representation},

language = {eng},

pages = {503-526},

publisher = {Springer - Lecture Notes in Mathematics},

title = {Spectral representation of isotropic random currents},

url = {http://eudml.org/doc/113698},

volume = {23},

year = {1989},

}

TY - JOUR

AU - Wong, Eugene

AU - Zakai, Moshe

TI - Spectral representation of isotropic random currents

JO - Séminaire de probabilités de Strasbourg

PY - 1989

PB - Springer - Lecture Notes in Mathematics

VL - 23

SP - 503

EP - 526

LA - eng

KW - isotropic random currents; homogeneity; isotropy; Ito's characterization of the spectral measure; spectral representation

UR - http://eudml.org/doc/113698

ER -

## References

top- [1] H. Flanders, Differential Forms, Academic Press, 1963. Zbl0112.32003MR162198
- [2] K. Ito, "isotropic random current," Proceedings, Third Berkeley Symp. on Math. Stat. and Prob., 1956, pp. 125-32. Zbl0071.13201MR84890
- [3] S. Ito, "On the canonical form of turbulence," Nagoya Math. J., vol. 2, 1951, pp. 83-92. Zbl0042.43303MR40619
- [4] V. Mandrekar, "Markov properties of random fields," Probabilistic Analysis and Related Topics, vol. 3, pp. 161-193, A.T. Bharucha-Reid (ed.), Academic Press, 1983. Zbl0547.60055MR748856
- [5] G. deRham, Differentiable Manifolds, Springer-Verlag, 1982. Zbl0534.58003
- [6] Y.A. Rozanov, Markov Random Fields, Academic Press, 1982. MR676644
- [7] L. Schwartz, Theory des distributions, Herman, 1966.
- [8] C. von Westenholtz, Differential Forms in Mathematical Physics, North Holland, 1981. Zbl0391.58001MR641034
- [9] E. Wong and B. Hajek, Stochastic Processes in Engineering Systems, Springer-Verlag, 1985. Zbl0545.60003MR787046
- [10] E. Wong and M. Zakai, "Markov processes on the plane," Stochastics, vol. 15, 1985, pp. 311-333. Zbl0588.60043MR826989
- [11] E. Wong and M. Zakai, "Martingale differential forms," Prob. Th. Rel. Fields, vol. 74, 1987, pp. 429-453. Zbl0612.60045MR873888
- [12] E. Wong and M. Zakai, "Isotropic Gauss Markov currents," to appear in Prob. Th. Rel. Fields. Zbl0659.60120MR997434
- [13] A.M. Yaglom, "Some classes of random fields in n-dimensional space related to stationary random processes , "Theory of Probability and Its Applications, vol. 2, 1957, pp. 273-320.
- [14] A.M. Yaglom, Correlation theory of stationary and related random functions. Vol. I, II. Springer-Verlag, New York, 1987 Zbl0685.62077

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