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| POSITIVE MARTINGALES AND RANDOM MEASURES |
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Citation： |
Kahane Jean-Pierre.POSITIVE MARTINGALES AND RANDOM MEASURES[J].Chinese Annals of Mathematics B,1987,8(1):1~12 |
| Page view： 1711
Net amount： 853 |
Authors： |
Kahane Jean-Pierre; |
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| Abstract： |
Given Q_n(t) (n=0, 1,\cdots), a positive martingale indexed by t (t\in T, compact metric space) and a measure \sigma \in M^+(T), the random measure Q\sigma is defined as a limit of Q_n\sigma. In general EQ\sigma \leq \sigma. Conditions are given to insure either EQ\sigma=0 (degeneracy) or EQ\sigma=\sigma(full action). In the particular case when Q_n(t) a product of independent weight functions,\sigma is decomposed into a sum of two mutually singular measures,\sigma=\sigma'+\sigma'', such that Q acts fully on \sigma' and is degeneoate on \sigma'', and the operator EQ is a projection. Examples and applications aoe given (random covecings, B. Mandelbrot's martingales, multiplicative chaos). |
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