Random measure - Wikipedia

Abstraction: Measure-valued random element foundational for point processes

Key points:

• A random measure is a measure-valued random element; defined either as a locally finite transition kernel from a probability space or as a random element taking values in the space of locally finite measures
• The intensity measure E[mu(A)] is always a sigma-finite measure; the supporting measure is always finite
• Laplace functional L(f) = E[exp(-integral f d mu)] uniquely characterizes the distribution along with integrals over continuous compactly supported functions
• Measures decompose into diffuse (non-atomic) and purely atomic parts; a random counting measure (point process) is the purely atomic special case
• Poisson point processes and Cox processes are canonical examples of random measures
• Useful in Monte Carlo methods, particle filters, and stochastic analysis

Connections: Measure Theory · Point Process · Stochastic Processes

Source: http://en.wikipedia.org/wiki/Random_measure