Maximum of cumulative sums for the Cauchy distribution

V. B. Nevzorov

doi:10.1007/bf01240000

journal article Oct 01, 1982

Maximum of cumulative sums for the Cauchy distribution

V. B. Nevzorov

Journal of Soviet Mathematics Vol. 20 No. 3 pp. 2221-2224 · Springer Science and Business Media LLC

View at Publisher Save 10.1007/bf01240000

Topics

No keywords indexed for this article. Browse by subject →

References

14

[1]

The maximum of sums of stable random variables

D. A. Darling

Transactions of the American Mathematical Society 1956 10.1090/s0002-9947-1956-0080393-6

[2]

C. C. Heyde, ?On the maximum of sums of random variables and the supremum functional for stable processes,? J. Appl. Prob.,6, No. 2, 519?429 (1969). 10.2307/3212011

[3]

V. B. Nevzorov, ?On joint distributions of random variables connected with fluctuations of a stable process,? Teor. Veroyatn. Primen.,18, No. 1, 164?172 (1973).

[4]

A. A. Pecherskii and B. A. Rogozin, ?On joint distributions of random variables connected with fluctuations of a process with independent increments,? Teor. Veroyatn. Primen.,14, No. 3, 431?444 (1969).

[5]

P. Erdös and M. Kac, ?On certain limit theorems in the theory of probability,? Bull. Am. Math. Soc.,52, 292?302 (1946). 10.1090/s0002-9904-1946-08560-2

[6]

V. B. Nevzorov, ?On some estimates for the distribution of the maximum of cumulative sums,? Teor. Veroyatn. Mat. Statist., No. 5, 88?97 (1971).

[7]

T. V. Arak, ?On the distribution of cumulative sums of independent random variables,? Teor. Veroyatn. Primen.,19, No. 2, 257?277 (1974).

[8]

C. C. Heyde, ?A limit theorem for random walks with drift,? J. Appl. Prob.,4, No. 1, 144?150 (1967). 10.2307/3212307

[9]

B. A. Rogozin, ?The rate of convergence of the distribution of the maximum of sums of independent random variables to a limit law,? Teor. Veroyatn. Primen.,11, No. 3, 497?500 (1966).

[10]

V. Paulauskas and S. Steinshunas, ?On the rate of convergence of the distribution of the maximum of cumulative sums of independent, identically distributed random vectors to a limit law,? Litov. Mat. Sb.,13, No. 1, 139?147 (1973).

[11]

V. B. Nevzorov, ?On the nearness of the distribution of the maximum of cumulative sums of independent terms to the distribution of the last sum,? Teor. Veroyatn. Mat. Statist., No. 8, 106?109 (1973).

[12]

A. A. Borovkov, ?On factorization identities and properties of the distribution of the supremum of cumulative successive sums,? Teor. Veroyatn. Primen.,15, No. 3, 377?418 (1970).

[13]

A. K. Aleshkyavichene, ?Approximation of the distribution of the maximum of sums of random variables with a mean that is small in absolute value,? Dokl. Akad. Nauk SSSR,233, No. 6, 1017?1020 (1977).

[14]

V. B. Nevzorov, ?On a class of limit laws for the maximum of cumulative sums,? Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,72, 92?97 (1977).

Metrics

2

Citations

14

References

Details

Published: Oct 01, 1982
Vol/Issue: 20(3)
Pages: 2221-2224
License: View

Authors

V

V. B. Nevzorov

Cite This Article

V. B. Nevzorov (1982). Maximum of cumulative sums for the Cauchy distribution. Journal of Soviet Mathematics, 20(3), 2221-2224. https://doi.org/10.1007/bf01240000

Maximum of cumulative sums for the Cauchy distribution

You May Also Like