scholarly journals Intrinsic fractional noise in nanopores: The effect of reservoirs

2021 ◽  
Vol 154 (17) ◽  
pp. 171101
Author(s):  
S. Marbach
Keyword(s):  
Fractional Noise

Analysis of the density of the solution to a semilinear SPDE with fractional noise

Stochastics ◽  
2016 ◽  
Vol 88 (7) ◽  
pp. 959-979 ◽  
Author(s):  
Junfeng Liu ◽  
Ciprian A. Tudor
Keyword(s):  
Fractional Noise

scholarly journals Intermittency for the wave and heat equations with fractional noise in time

2016 ◽  
Vol 44 (2) ◽  
pp. 1488-1534 ◽  
Author(s):  
Raluca M. Balan ◽  
Daniel Conus
Keyword(s):  
Heat Equations ◽  
Fractional Noise

scholarly journals SOME LINEAR SPDEs DRIVEN BY A FRACTIONAL NOISE WITH HURST INDEX GREATER THAN 1/2

2012 ◽  
Vol 15 (04) ◽  
pp. 1250023 ◽  
Author(s):  
RALUCA M. BALAN
Keyword(s):  
Stable Process ◽  
Sufficient Conditions ◽  
Hyperbolic Type ◽  
Hurst Index ◽  
Intersection Local Time ◽  
Fractional Noise ◽  
Spatial Operator ◽  
Parabolic Case ◽  
Spatially Homogeneous ◽  
Necessary And Sufficient

In this article, we identify the necessary and sufficient conditions for the existence of a random field solution for some linear stochastic partial differential equations (spde's) of parabolic and hyperbolic type. These equations rely on a spatial operator [Formula: see text] given by the L2-generator of a d-dimensional Lévy process X = (Xt)t≥0, and are driven by a spatially-homogeneous Gaussian noise, which is fractional in time with Hurst index H > 1/2. As an application, we consider the case when X is a β-stable process, with β ∈ (0, 2]. In the parabolic case, we develop a connection with the potential theory of the Markov process [Formula: see text] (defined as the symmetrization of X), and we show that the existence of the solution is related to the existence of a "weighted" intersection local time of two independent copies of [Formula: see text].

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