Hyperbolic Harmonic Functions and Hyperbolic Brownian Motion
نویسندگان
چکیده
منابع مشابه
Hyperbolic branching Brownian motion
Hyperbolic branching Brownian motion is a branching di usion process in which individual particles follow independent Brownian paths in the hyperbolic plane H2, and undergo binary ssion(s) at rate ¿0. It is shown that there is a phase transition in : For 51=8 the number of particles in any compact region of H2 is eventually 0, w.p.1, but for ¿1=8 the number of particles in any open set grows to...
متن کاملHarmonic functions on hyperbolic graphs
We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The proof is inspired by the works of F. Mouton in the cases of Riemannian manifolds of pinched negative curvature and infinite trees. It involves geometric and ...
متن کاملBrownian Motion and Harmonic Functions
The Lie group Sol(p, q) is the semidirect product induced by the action of R on R which is given by (x, y) 7→ (ex, e−qzy), z ∈ R. Viewing Sol(p, q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with drift. We derive a central limit theorem and...
متن کاملOn characterizations of hyperbolic harmonic Bloch and Besov spaces
We define hyperbolic harmonic $omega$-$alpha$-Bloch space $mathcal{B}_omega^alpha$ in the unit ball $mathbb{B}$ of ${mathbb R}^n$ and characterize it in terms of $$frac{omegabig((1-|x|^2)^{beta}(1-|y|^2)^{alpha-beta}big)|f(x)-f(y)|}{[x,y]^gamma|x-y|^{1-gamma}},$$ where $0leq gammaleq 1$. Similar results are extended to little $omega$-$alpha$-Bloch and Besov spaces. These obtained...
متن کاملON THE SHEARLET TRANSFORM USING HYPERBOLIC FUNCTIONS
In this paper, we focus on the study of shearlet transform which isdened by using the hyperbolic functions. As a result we check an admissibilitycondition such that implies the reconstruction formula. To this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Clifford Algebras
سال: 2020
ISSN: 0188-7009,1661-4909
DOI: 10.1007/s00006-020-01099-z