arXiv subjects

V. Mandrekar

Publications and source records attributed to V. Mandrekar.

2 recordsLinked to original sources

arXiv2016

Ito formula for mild solutions of SPDEs with Gaussian and non-Gaussian noise and applications to stability properties

We use Yosida approximation to find an It\^o formula for mild solutions $\left\{X^x(t), t\geq 0\right\}$ of SPDEs with Gaussian and non-Gaussian coloured noise, the non Gaussian noise being defined through compensated Poisson random measure associated to a L\'evy process. The functions to which we apply such It\^o formula are in $C^{1,2}([0,T]\times H)$, as in the case considered for SDEs in [9]. Using this It\^o formula we prove exponential stability and exponential ultimate boundedness properties in mean square sense for mild solutions. We also compare such It\^o formula to an It\^o formula for mild solutions introduced by Ichikawa in [8], and an It\^o formula written in terms of the semigroup of the drift operator [11] which we extend before to the non Gaussian case.

math.PR↗

arXiv2012

On the mixing structure of stationary increment and self-similar symmetric α-stable processes

Mixed moving average processes appear in the ergodic decomposition of stationary symmetric α-stable (SαS) processes. They correspond to the dissipative part of "deterministic" flows generating SαS processes (Rosinski, 1995). Along these lines we study stationary increment and self-similar SαS processes. Since the classes of stationary increment and self-similar processes can be embedded into the class of stationary processes by the Masani and Lamperti transformations, respectively, we characterize these classes of SαS processes in terms of nonsingular flows and the related cocycles. We illustrate this approach considering various examples of self-similar mixed moving average SαS processes introduced in (Surgailis, Rosinski, Mandrekar and Cambanis, 1992).

math.PR↗