Abstract
This article deals with a class of random measures formed of doubly stochastic marked random measures that assumes parameters in accordance with the evolution of some stochastic process, called a “modulator.” Throughout the paper, restrictions imposed on random measures (to be modulated) and the modulator are kept to a minimum. One of the objective of these studies are intensities and reward rates of modulated random measures that can play a significant role in stochastic control and optimization. Analytically tractable formulas for such functionals are obtained and examples and applications are discussed and treated in details.
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