A new path integration method for the stochastic system under Poisson white noise excitation based on a probability mapping

In this paper, a new path integration method is proposed for stochastic dynamical systems excited by Poisson white noise. An efficient one-step transition probability density function (TPDF) matrix is constructed based on a decoupling probability mapping. The new method can handle the case of multiple impulses occurring in a one-step transition time interval and considers the randomness of the impulse instant, which compensates for a drawback of previous path integration methods. The probability mapping realizes the decoupling of randomness and the one-step TPDF matrix, which can be extended to general stochastic systems satisfying the Markov property. The stochastic responses of two dynamical systems excited by Poisson white noises for different mean arrival rates are obtained by using the new path integration method, and MC simulations prove that the new method is very effective, and it maintains good accuracy even for large mean arrival rates.