On some characterization problems connected with stochastic integrals.
Authors:
Robert Iugannani and John B. Thomas
Journal:
Quart. Appl. Math. 29 (1971), 53-63
MSC:
Primary 60.75
DOI:
https://doi.org/10.1090/qam/288872
MathSciNet review:
288872
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V. P. Skitovič, On a characterization of Brownian motion, Teor. Verojatnost i Primenen. 1, 361–364 (1956); Theor. Probability Appl. 1, 326–328 (1956)
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G. Darmois, Analyse générale des liasions stochastiques, Étuder particulière de l’analyse factorielle linéaire, Rev. Inst. Internat. Statistique 21, 2–8 (1953)
V. P. Skitovič, Linear combinations of independent random variables and the normal distribution, Izv. Akad. Nauk SSSR Ser. Mat. 18, 185–200 (1954); English transl., Selected Transl. Math. Stat. and Prob., vol. 2, Amer. Math. Soc., Providence, R. I., 1961, pp. 211–228
C. R. Rao, On some characterizations of the normal law, Sankhyā Ser. A 29, 1–14 (1967)
R. G. Laha, On a characterization of the normal distribution from properties of suitable linear statistics, Ann. Math. Statist. 28, 126–139 (1957)
T. Cacoullos, Characterizations of normality by constant regression of linear statistics on another linear statistic, Ann Math. Statist. 38, 1894–1898 (1967)
---, Some characterizations of normality, Sankhyā Ser. A 29, 399–404 (1967)
R. G. Laha and E. Lukacs, On a linear form whose distribution is identical with that of a monomial, Pacific J. Math 15, 207–214 (1965)
Yu. V. Linnik, Linear forms and the statistical criteria. I, II, Ukrain. Mat. Ž. 5, 207–243, 247–290; (1953); English transl., Selected Transl. Math. Stat. and Prob., vol. 3, Amer. Math. Soc., Providence, R. I., 1963, pp. 1–90
L. V. Mamaǐ, On the theory of characteristic functions, Vestnik Leningrad. Univ. 15, no. 1, 85–99; (1960), English transl., Selected Transl. Math. Stat. and Prob., vol. 4, Amer. Math. Soc., Providence, R. I., 1963, pp. 153–170
J. Marcinkiewicz, Sur une proprété de la loi de Gauss, Math. Z. 44, 612–618 (1938)
V. P. Skitovič, On a characterization of Brownian motion, Teor. Verojatnost i Primenen. 1, 361–364 (1956); Theor. Probability Appl. 1, 326–328 (1956)
R. G. Laha and E. Lukacs, On identically distributed stochastic integrals, Trans. Third Prague Conf. Information Theory, Statist. Decision Functions, Random Processes (Liblice, 1962), Publ. House Czech. Acad. Sci., Prague, 1964, pp. 467–474
E. Lukacs and R. G. Laha, Applications of characteristic functions, Griffin’s Statistical Monographs and Courses, no. 14, Hafner, New York, 1964
R. Lugannani and J. B. Thomas, On a class of stochastic processes which are closed under linear transformations, Information and Control 10, 1–21 (1967)
P. A. Pierre, Characteristics of Gaussian random processes by representations in terms of independent random variables, IEEE Trans. Information Theory 15, 648–658 (1969)
A. V. Balakrishnan, Communication theory, McGraw-Hill, New York, 1968
W. B. Davenport, Jr. and W. L. Root, An introduction to the theory of random signals and noise, McGraw-Hill, New York, 1958
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© Copyright 1971
American Mathematical Society