Title
Itô formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties
Document Type
Article
Publication Date
12-30-2016
Publication Title
arXiv:1612.09440 [math.PR]
Abstract
We use Yosida approximation to find an Itô formula for mild solutions { Xx(t), t ≥ 0 }of SPDEs with Gaussianand non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a Lévy process. The functions to which we apply such Itô formula are in C1,2([0,T]×H), as in the case considered for SDEs in [19]. Using this Itô formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such Itô formula to an Itô formula for mild solutions introduced by Ichikawain [15], and an Itô formula written in terms of the semigroup of the drift operator [6] which we extend before to the non Gaussian case.
Volume
1
First Page
1
Last Page
36
Rights
© 2016 arXiv.org
Recommended Citation
Albeverio, Sergio; Gawarecki, Leszek; Mandrekar, Vidyadhar; Rüdiger, Barbara; and Sarkar, Barun, "Itô formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties" (2016). Mathematics Publications. 6.
https://digitalcommons.kettering.edu/mathematics_facultypubs/6
