## Electronic Communications in Probability

### Spectral densities related to some fractional stochastic differential equations

#### 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

#### 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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