Electronic Communications in Probability

Spectral densities related to some fractional stochastic differential equations

Mirko D’Ovidio, Enzo Orsingher, and Ludmila Sakhno

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Abstract

In this paper we consider fractional higher-order stochastic differential equations of the form \[ \left ( \mu + c_\alpha \frac{d^\alpha } {dt^\alpha } \right )^\beta X(t) = \mathcal{E} (t) , \quad \mu >0,\; \beta >0,\; \alpha \in (0,1) \cup \mathbb{N} \] where $\mathcal{E} (t)$ is a Gaussian white noise. We obtain explicitly the covariance functions and the spectral densities of the stochastic processes satisfying the above equations.

Article information

Source
Electron. Commun. Probab. Volume 21 (2016), paper no. 18, 15 pp.

Dates
Received: 7 July 2015
Accepted: 17 February 2016
First available in Project Euclid: 25 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1456412898

Digital Object Identifier
doi:10.1214/16-ECP4411

Zentralblatt MATH identifier
1343.60071

Subjects
Primary: 60K99: None of the above, but in this section 60G60: Random fields

Keywords
higher-order heat equations Weyl fractional derivatives airy functions spectral densities

Rights
Creative Commons Attribution 4.0 International License.

Citation

D’Ovidio, Mirko; Orsingher, Enzo; Sakhno, Ludmila. Spectral densities related to some fractional stochastic differential equations. Electron. Commun. Probab. 21 (2016), paper no. 18, 15 pp. doi:10.1214/16-ECP4411. https://projecteuclid.org/euclid.ecp/1456412898.


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