### Abstract

Many of the classical submartingale inequalities, including Doob's maximal inequality and upcrossing inequality, are valid for sequences S_{j} such that the (S_{j+1}-S_{j}'s are associated (positive mean) random variables, and for more general "demisubmartingales". The demisubmartingale maximal inequality is used to prove weak convergence to the two-parameter Wiener process of the partial sum processes constructed from a stationary two-parameter sequence of associated random variables X_{ij}with {Mathematical expression}.

Original language | English (US) |
---|---|

Pages (from-to) | 361-371 |

Number of pages | 11 |

Journal | Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete |

Volume | 59 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1982 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Analysis
- Mathematics(all)

### Cite this

*Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete*,

*59*(3), 361-371. https://doi.org/10.1007/BF00532227

**Associated random variables and martingale inequalities.** / Newman, C. M.; Wright, A. L.

Research output: Contribution to journal › Article

*Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete*, vol. 59, no. 3, pp. 361-371. https://doi.org/10.1007/BF00532227

}

TY - JOUR

T1 - Associated random variables and martingale inequalities

AU - Newman, C. M.

AU - Wright, A. L.

PY - 1982/9

Y1 - 1982/9

N2 - Many of the classical submartingale inequalities, including Doob's maximal inequality and upcrossing inequality, are valid for sequences Sj such that the (Sj+1-Sj's are associated (positive mean) random variables, and for more general "demisubmartingales". The demisubmartingale maximal inequality is used to prove weak convergence to the two-parameter Wiener process of the partial sum processes constructed from a stationary two-parameter sequence of associated random variables Xijwith {Mathematical expression}.

AB - Many of the classical submartingale inequalities, including Doob's maximal inequality and upcrossing inequality, are valid for sequences Sj such that the (Sj+1-Sj's are associated (positive mean) random variables, and for more general "demisubmartingales". The demisubmartingale maximal inequality is used to prove weak convergence to the two-parameter Wiener process of the partial sum processes constructed from a stationary two-parameter sequence of associated random variables Xijwith {Mathematical expression}.

UR - http://www.scopus.com/inward/record.url?scp=0001256747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001256747&partnerID=8YFLogxK

U2 - 10.1007/BF00532227

DO - 10.1007/BF00532227

M3 - Article

AN - SCOPUS:0001256747

VL - 59

SP - 361

EP - 371

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3

ER -