X-Nico

Point process

The joint intensities of a point process $\backslash xi$ w.r.t. the Lebesgue measure are functions $\backslash rho^\{(k)\}\; :(\backslash mathbb\{R\}^d)^k\; \backslash to\; 0,\backslash infty)$ such that for any disjoint bounded Borel subsets $B\; 1,\backslash ldots,B\; k$

•

While in the exact mathematical definition a point pattern is specified as a locally finite counting measure, it is sufficient for more applied purposes to think of a point pattern as a countable subset of S that has no limit points.

•

where $\backslash delta$ denotes the Dirac measure, N is an integer-valued random variable and $X\; i$ are random elements of S.

see also