Search results for "Chapman–Kolmogorov equation"

Path integral solution for non-linear system enforced by Poisson White Noise

2008

Abstract In this paper the response in terms of probability density function of non-linear systems under Poisson White Noise is considered. The problem is handled via path integral (PI) solution that may be considered as a step-by-step solution technique in terms of probability density function. First the extension of the PI to the case of Poisson White Noise is derived, then it is shown that at the limit when the time step becomes an infinitesimal quantity the Kolmogorov–Feller (K–F) equation is fully restored enforcing the validity of the approximations made in obtaining the conditional probability appearing in the Chapman Kolmogorov equation (starting point of the PI). Spectral counterpa…

The Master Equation

2009

Stochastic ship roll motion via path integral method

2010

ABSTRACTThe response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple …