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Martingales and stochastic integrals for processes with a multi- dimensional parameter. (English) Zbl 0282.60030


MSC:

60H05 Stochastic integrals
60G15 Gaussian processes
93E10 Estimation and detection in stochastic control theory
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[1] Cairoli, R., Une inegalité pour martingales à indices multiples et ses applications, Lecture Notes in Mathematics 124, 1-27 (1970), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0218.60045
[2] Cairoli, R., Sur une équation différentielle stochastique, Compte Rendus Acad. Sc. Paris, 274, 1739-1742 (1972) · Zbl 0244.60045
[3] Cameron, R. H.; Martin, W. T., The orthogonal development of nonlinear functionals in a series of Fourier-Hermite functions, Ann. of Math., 48, 385-392 (1947) · Zbl 0029.14302
[4] Clark, J. M. C., The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Statist, 41, 1282-1295 (1970) · Zbl 0213.19402
[5] Doléans-Dade, C.; Meyer, P. A., Intégrales stochastiques par rapport aux martingales locale, Lecture Notes in Mathematics, 124, 77-107 (1970), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0211.21901
[6] Ito, K., Multiple Wiener integral, J. Math. Soc. Japan, 3, 157-169 (1951) · Zbl 0044.12202
[7] Kunita, H.; Watanabe, S., On square integrable martingales, Nagoya Math. J., 30, 209-245 (1967) · Zbl 0167.46602
[8] Park, W. J., A multiparameter Gaussian process, Ann. Math. Statist., 4, 1582-1595 (1970) · Zbl 0279.60030
[9] Yeh, J., Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc., 95, 443-450 (1960) · Zbl 0201.49402
[10] Yeh, J., Cameron-Martin translation theorems in the Wiener space of functions of two variables, Trans. Amer. Math. Soc., 107, 409-420 (1963) · Zbl 0113.33104
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