Author:
Rajkumar Rahul,Weisbart David
Abstract
AbstractThe fundamental solution to a pseudo-differential equation for functions defined on the d-fold product of the p-adic numbers, $$\mathbb {Q}_p$$
Q
p
, induces an analogue of the Wiener process in $$\mathbb {Q}_p^d$$
Q
p
d
. As in the real setting, the components are 1-dimensional p-adic Brownian motions with the same diffusion constant and exponent as the original process. Asymptotic analysis of the conditional probabilities shows that the vector components are dependent for all time. Exit time probabilities for the higher dimensional processes reveal a concrete effect of the component dependency.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Mathematics,Analysis
Reference38 articles.
1. Albeverio, S., Karwowski, W.: A random walk on $$p$$-adics—the generator and its spectrum. Stoch. Process. Appl. 53, 1–22 (1994)
2. Antoniouk, A.V., Khrennikov, A.Y., Kochubei, A.N.: Multidimensional nonlinear pseudo-differential evolution equation with $$p$$-adic spatial variables. J. Pseudo-Differ. Oper. Appl. 11, 311–343 (2020)
3. Avetisov, V.A., Bikulov, A.K.: On the ultrametricity of the fluctuation dynamic mobility of protein molecules. Proc. Steklov Inst. Math. 265(1), 75–81 (2009)
4. Avetisov, V.A., Bikulov, A.K., Kozyrev, S.V.: Application of $$p$$-adic analysis to models of breaking of replica symmetry. J. Phys. A. 32(50), 8785–8791 (1999)
5. Avetisov, V.A., Bikulov, A.K., Kozyrev, S.V.: Description of logarithmic relaxation by a model of a hierarchical random walk. Dokl. Akad. Nauk 368(2), 164–167 (1999)
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