Convergence And Application For Negatively Associated Random Variable Series

Limiting behavior of random variable series is a brand of important theory in probability. For independent random variable series or mixing association random variable series, the strong law of large numbers and the strong stability is extensively studied by many authors in recent years. But negative association random variable series is a kind of important random variable series and it is very useful of application in probability and stastic. Thus it is necessary to study the convergence for a class of negative association random variable series. It has been an active research area about this aspect, a flood of papers have been published on this topic up to today. For example,the studying of NQD random variable series、NA random variable series, etc., these kinds of negatively associated random variable series.The thesis is a research on the convergence and application for negatively associated random variable series. The whole thesis contains four parts.In the first part, we define a extensive class of negative association random variable series. Also we introduce a few of history backdrop and interrelated con-clusions of the strong stability of linear forms for NQD random variable series NA random variable series.In the second part, we mainly study the strong law of large numbers for a class of negative association random variable series that we define in the first part. We have lots of important theories of a class of negative association random variable series, also those conclusions extend the condition of NQD random variable series.In the third part, we mainly study strong stability of linear forms in a class of negatively dependent random variable series and get sufficient conditions for strong stability of linear forms with different distributions random variable series.In the last part, we mainly study the log-optimal portfolio. Allowed short sale discrete-time finance markets are investigated under one-period and multi-period circumstances. Using the basic properties of conditional expectation and the con-vergence theorem of a class of negative association random variable series, we get some properties about log-optimal portfolio when the markets satisfy a class of negative association random variable series from two aspects:with risk control and without risk control.