Search results for "Probability-generating function"
showing 3 items of 3 documents
Stationary and non-stationary probability density function for non-linear oscillators
1997
A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.
Analysis of random walks on a hexagonal lattice
2019
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a 2-dimensional Brownian motion is also discussed. Furthermore, we obtain some results on its asymptotic behavior making use of large deviation theory. Finally, we investigate the first-passage-time problem of the random walk through a vertical straight-line. Under suitable symmetry assumptions we are able to determine the first-passage-time probabilities in a closed form, which deserve interest in applied fields.
Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates
2021
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subodinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in Di Crescenzo A., Macci C., Martinucci B. (2014).