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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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

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

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

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

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

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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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