Lévy Processes in the Physical Sciences

By Wojbor A. Woyczynski. 2001

165 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8f3e7c5846c0d9993b748106e8c75f9aababa96e

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In Condensed Matter Physics

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Citations in the corpus

Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations (2015, background): “Among these, we mention obstacle problems [10], finance [16], quasi-geostrophic flows [11, 15], anomalous diffusion [27, 37, 39].”
A Tail-Index Analysis of Stochastic Gradient Noise in Deep Neural Networks (2019, background): “Even though the finite-variance assumption seems natural and intuitive at the first sight, it turns out that in many domains, such as turbulent motions [52], oceanic fluid flows [53], finance [35], biological evolution [26], audio signals [34], the assumption might fail to hold (see [13] for more ex”
Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, background): “The rigorous study of such nonlinear models has been delayed until this time by the mathematical difficulties in treating at the same time the nonlinearity and fractional diffusion.”
Models of anomalous diffusion: the subdiffusive case (2005, background): “…equations involving derivatives of fractional orders, their physically and computationally useful theory is still only in their beginning stage, especially in the case of nonlinear fractional phenomena, see, e.g., Biler, Funaki and Woyczynski (1999), and Biler, Karch and Woyczynski (2001).”
Second-order elliptic integro-differential equations: viscosity solutions' theory revisited (2007, background): “3 Examples of PIDE A first example of (semilinear) PIDE is one appearing in the context of growing interfaces [21]”
Nonlocal Diffusion and Applications (2015, background): “obabilisticprocessapproachesafractionalheatequation. Weobservethatprocessesofthistypeoccurinnaturequiteoften,seeinparticular the biological observations in [140,91], other interesting observations in [118,126,142]andthemathematicaldiscussionsin[94,85,110,105,108]. Roughly speaking, let us say that i”