Abstract
We study a one-dimensional stochastic differential equation with linear damping, in the presence of both additive and multiplicative noise. We consider the case in which the additive noise is white and the multiplicative noise has a power law spectrum. It is shown that for negative values of the exponent in the multiplicative noise spectrum all the moments of the solution to the stochastic equation diverge, while for positive values the moments are all finite. When the exponent is zero, corresponding to white multiplicative noise, the moments are finite when their order is smaller than the ratio of the dissipation to the multiplicative noise strength.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
