For , where are mutually independent fractional Brownian motions, we obtain the exact asymptotics of where is a non-singular matrix and , are such that there exists some such that
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http://dx.doi.org/10.1007/s10687-024-00489-x | DOI Listing |
Phys Rev E
November 2024
Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California 90089-2531, USA.
Statistics of diffusion, modeled by random walks, such as the mean number of distinct sites visited S(t) at time t, the mean probability P_{0}(t) of being at the origin of the walk, and the mean-squared displacements 〈R^{2}(t)〉 of the random walkers have been studied extensively in the past in both regular lattices and such disordered media as percolation clusters and other fractal structures, and universal power laws for such quantities have been derived. S(t) provides insight into reaction properties of geological formations, while P_{0}(t) is directly linked with the problem of back diffusion in remediation of groundwater aquifers. In all such studies, it was assumed that the conductances of the bonds that connect nearest-neighbor sites of the lattices are equal.
View Article and Find Full Text PDFChaos
December 2024
Department of Physics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Park Komenského 2, Košice 042 00, Slovakia.
The generalized Langevin equation (GLE) for a tagged particle in a liquid of charged particles under the influence of external AC electric fields is studied. For the fractional memory kernel in the GLE, the mean square displacement (MSD) of the particle is studied analytically in both the underdamped and overdamped regimes. The MSD consists of a part corresponding to the absence of the external field and a part affected by the external field, which is expressed through the mean velocity of the particle.
View Article and Find Full Text PDFPhys Rev E
October 2024
Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France.
We compute the connected two-time correlator of the maximum M_{N}(t) of N independent Gaussian stochastic processes (GSPs) characterized by a common correlation coefficient ρ that depends on the two times t_{1} and t_{2}. We show analytically that this correlator, for fixed times t_{1} and t_{2}, decays for large N as a power law N^{-γ} (with logarithmic corrections) with a decorrelation exponent γ=(1-ρ)/(1+ρ) that depends only on ρ, but otherwise is universal for any GSP. We study several examples of physical processes including the fractional Brownian motion (fBm) with Hurst exponent H and the Ornstein-Uhlenbeck process (OUP).
View Article and Find Full Text PDFExtremes (Boston)
August 2024
Department of Actuarial Science, University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland.
For , where are mutually independent fractional Brownian motions, we obtain the exact asymptotics of where is a non-singular matrix and , are such that there exists some such that
View Article and Find Full Text PDFSci Rep
October 2024
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia.
This study dynamically investigates the mathematical Ivancevic option pricing governing system in terms of conformable fractional derivative, which illustrates a confined Brownian motion identified with a non-linear Schrödinger type equation. This model describes the controlled Brownian motion that comes with a non-linear Schrödinger type equation. The solution to comprehend the market price fluctuations for the suggested model is developed through the application of a mathematical strategy.
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