Open Access
2016 Spectral densities related to some fractional stochastic differential equations
Mirko D’Ovidio, Enzo Orsingher, Ludmila Sakhno
Electron. Commun. Probab. 21: 1-15 (2016). DOI: 10.1214/16-ECP4411


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.


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Mirko D’Ovidio. Enzo Orsingher. Ludmila Sakhno. "Spectral densities related to some fractional stochastic differential equations." Electron. Commun. Probab. 21 1 - 15, 2016.


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

zbMATH: 1343.60071
MathSciNet: MR3485387
Digital Object Identifier: 10.1214/16-ECP4411

Primary: 60G60 , 60K99

Keywords: Airy functions , higher-order heat equations , spectral densities , Weyl fractional derivatives

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