On probability and moment inequalities for supermartingales and martingales

Acta Applicandae Mathematicae

Volumn 97, Issue 1-3, 2007, Pages 151-162

  Nagaev, S V ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

Holder inequality; Jensen inequality; Martingale; Submartingale; Supermartingale

Indexed keywords

MATHEMATICAL OPERATORS; NUMERICAL METHODS; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; STATISTICAL TESTS;

HOLDER INEQUALITY; JENSEN INEQUALITY; MARTINGALE; SUBMARTINGALE; SUPERMARTINGALE;

RANDOM VARIABLES;

EID: 34248531479     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-007-9131-0     Document Type: Article

References (18)

1. Nagaev, S.V.: On probability and moment inequalities for supermartingales and martingales. Acta Appl. Math. 79, 35-46 (2003)
2. Nagaev, S.V.: On probability and moment inequalities for supermartingales and martingales. Teor. Veroyatn. i Primenen. 51(2), 391-400 (2006)
3. Burkholder: Distribution function inequalities for martingales. Ann. Probab. 1, 19-42 (1973)
4. Hitczenko, P.: Best constants in martingale version of Rosenthal's inequality. Ann. Probab. 18, 1656-1668 (1990)
5. Johnson, W.B., Schechtman, G., Zinn, J.: Best constants in moment inequalities for linear combination of independent and exchangeable random variables. Ann. Probab. 13, 234-253 (1985)
6. Nagaev, S.V.: Some refinements of probabilistic and moment inequalities. Teor. Veroyatn. i Primenen. 42(4), 832-838 (1997)
7. Shiryaev, A.N.: Probability. Nauka, Moscow (1989), 574 p.
8. Fuc, D.H., Nagaev, S.V.: Probability inequalities for sums of independent random variables. Teor. Veroyatn. i Primenen. 16(4), 660-675 (1971)
9. Foster, J.I.: A limit theorem for a branching process with state-dependent immigration. Ann. Math. Stat. 42(5), 1773-1776 (1971)
10. Nagaev, S.V., Khan, L.V.: Limit theorems for a critical Gallon-Watson process with migration. Teor. Veroyatn. i Primenen. 25(3), 523-534 (1980)
11. Shiryaev, A.N.: Foundation of Stochastic Financial Mathematics, vols. 1, 2. Fasis, Moscow (1998) (in Russian)
12. Whittle, P.: Bounds for the moments of linear and quadratic forms in independent variables. Teor. Veroyatn. i Primenen. 5(3), 331-334 (1960)
13. Dharmadhikari, S.W., Jogdeo, K.: Bounds on moments of certain random variables. Ann. Math. Stat. 40(4), 1506-1508 (1969)
14. Petrov, V.V.: Limit Theorems for Sums of Independent Random Variables. Nauka, Moscow (1987), 317 p.
15. Vatutin, V.A., Topchii, V.A.: The maximum of critical Galton-Watson processes and continuous from the left random walks. Teor. Veroyatn. i Primenen. 42(1), 21-34 (1997)
16. Pittenger, A.O.: Note on a square function inequality. Ann. Probab. 7, 907-908 (1979)
17. Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis. Cambridge University Press, Cambridge (1927)
18. Doob, J.L.: Stochastic Processes. Wiley, New York (1953)