On exact time averages of a massive Poisson particle

In this work we study, under the Stratonovich definition, the problem of the damped oscillatory massive particle subject to a heterogeneous Poisson noise characterized by a rate of events, lambda(t), and a magnitude, Phi, following an exponential distribution. We tackle the problem by performing exact time averages over the noise in a similar way to previous works analysing the problem of the Brownian particle. From this procedure we obtain the long-term equilibrium distributions of position and velocity as well as analytical asymptotic expressions for the injection and dissipation of energy terms. Considerations on the emergence of stochastic resonance in this type of system are also set forth.

Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ)

Faperj

CNPq

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

National Institute of Science and Technology for Complex Systems

National Institute of Science and Technology for Complex Systems

European Commission

European Commission[FP7-PEOPLE-2009-IEF]

European Commission

European Commission[250589]

Brazilian funding agency FAPESP

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)