Time-Changed Processes Governed by Space-Time Fractional Telegraph Equations |
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Authors: | Mirko D’ovidio Enzo Orsingher |
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Institution: | 1. Department of Basic and Applied Sciences for Engineers, Sapienza University of Rome, Rome, Italy;2. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy |
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Abstract: | We study global and local stabilities of the stationary zero solution to certain infinite-dimensional stochastic differential equations. The stabilities are in terms of fractional powers of the linear part of the drift. The abstract results are applied to semilinear stochastic partial differential equations with non-Lipschitzian drift terms and, in particular, to some specific models of population dynamics. We also expose the stabilizing effect of noise on the otherwise unstable zero solution As a basic tool we use the Forward Inequality, a generalization of Kolmogorov's forward equation; it is an application of Lyapunov's second method with a sequence of Lyapunov functionals |
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Keywords: | Riemann-Liouville fractional calculus Telegraph processes Stable positively skewed r v ’s Subordinators Fractional Laplacian Mittag-Leffler functions Time-changed processes Airy functions |
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