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
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- G. Darmois, Analyse générale des liaisons stochastiques. Etude particulière de l’analyse factorielle linéaire, Rev. Inst. Internat. Statist. 21 (1953), 2–8 (French). MR 61322
- V. P. Skitovič, Linear combinations of independent random variables and the normal distribution law, Select. Transl. Math. Statist. and Probability, Vol. 2, American Mathematical Society, Providence, R.I., 1962, pp. 211–218. MR 0150875
- C. Radhakrishna Rao, On some characterisations of the normal law, Sankhyā Ser. A 29 (1967), 1–14. MR 221559
- R. G. Laha, On a characterization of the normal distribution from properties of suitable linear statistics, Ann. Math. Statist. 28 (1957), 126–139. MR 83833, DOI https://doi.org/10.1214/aoms/1177707041
- Theophilos Cacoullos, Characterizations of normality by constant regression of linear statistics on another linear statistic, Ann. Math. Statist. 38 (1967), 1894–1898. MR 220328, DOI https://doi.org/10.1214/aoms/1177698623
- Theophilos Cacoullos, Some characterizations of normality, Sankhyā Ser. A 29 (1967), 399–404. MR 226698
- R. G. Laha and E. Lukacs, On a linear form whose distribution is identical with that of a monomial, Pacific J. Math. 15 (1965), 207–214. MR 179824
- Yu. V. Linnik, Linear forms and statistical criteria. I, II, Ukrain. Mat. Žurnal 5 (1953), 207–243, 247–290 (Russian). MR 0060767
- L. V. Mamaĭ, On the theory of characteristic functions, Vestnik Leningrad. Univ. 15 (1960), no. 1, 85–99 (Russian, with English summary). MR 0111990
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 Eugene 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. MR 0168011
- E. Lukacs and R. G. Laha, Applications of characteristic functions, Griffin’s Statistical Monographs & Courses, No. 14, Charles Griffin & Co., Ltd., London. Reprint of the 1964 original. MR 704969
- Robert Lugannani and John B. Thomas, On a class of stochastic processes which are closed under linear transformations, Information and Control 10 (1967), 1–21. MR 210186
- Percy A. Pierre, Characteristics of Gaussian random processes by representations in terms of independent random variables, IEEE Trans. Inform. Theory IT-15 (1969), 648–658. MR 297014, DOI https://doi.org/10.1109/tit.1969.1054387
A. V. Balakrishnan, Communication theory, McGraw-Hill, New York, 1968
- Wilbur B. Davenport Jr. and William L. Root, An introduction to the theory of random signals and noise, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1958. MR 0092275
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
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
60.75
Retrieve articles in all journals
with MSC:
60.75
Additional Information
Article copyright:
© Copyright 1971
American Mathematical Society
