Lp-intensities of random measures
Given a random measure [eta] and a fixed number p>1, the Lp-intensity ||[eta]||p of [eta]is defined as the total variation measure of the subadditive set function ||[eta](·)||p. It is shown that ||[eta]||p can exist (be locally finite) only if the usual intensity measure E[eta] exists and [eta] <<E[eta] a.s, and that in this case ||[eta]||pB=[small esh]B||d[eta]/dE[eta]||pdE[eta]. If [eta] is the conditional intensity of a simple point process [xi], then ||[eta]||p equals the total variation of the subadditive set functions ||P[[xi]B = 1Bc[xi]]||p and ||E[[xi]BBc[xi]]||p. Some applications to stochastic geometry and particle systems are discussed briefly.
Year of publication: |
1979
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Authors: | Kallenberg, Olav |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 9.1979, 2, p. 155-161
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Publisher: |
Elsevier |
Keywords: | Random measures absolute continuity conditional intensities particle systems total variation of subadditive set function |
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