Self-similarity and fractional Brownian motions on Lie groups
نویسندگان
چکیده
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this process has stationary increments and satisfies a local self-similar property. Furthermore the Lie groups for which this self-similar property is global are characterized .
منابع مشابه
HAGEN GILSING AND TOMMI SOTTINEN Power series expansions for fractional Brownian Motions
Fractional Brownian Motions (FBM) are selfsimilar Gaussian processes with hölder-continuous paths, that can be represented as fractional integrals (H > 12) or derivatives (H < 1 2) of Brownian Motions (BM), allow an stochastic calculus, have long-range memory and are of interest in finance and network traffic. For the theory and for the numerical simulation of FBM series expansions are of inter...
متن کاملExponents, symmetry groups and classification of operator fractional Brownian motions
Operator fractional Brownian motions (OFBMs) are zero mean, operator self-similar (o.s.s.), Gaussian processes with stationary increments. They generalize univariate fractional Brownian motions to the multivariate context. It is well-known that the so-called symmetry group of an o.s.s. process is conjugate to subgroups of the orthogonal group. Moreover, by a celebrated result of Hudson and Maso...
متن کاملIntegral representations and properties of operator fractional
Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar, and (iii) stationary increment processes. They are the natural multivariate generalizations of the well-studied fractional Brownian motions. Because of the possible lack of time reversibility, the defining properties (i)-(iii) do not, in general, characterize the covariance structure of OFBMs. To circumve...
متن کاملTokunaga and Horton self-similarity for level set trees of Markov chains
The Horton and Tokunaga branching laws provide a convenient framework for studying self-similarity in random trees. The Horton self-similarity is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity addresses so-called side branching. The Horton and Tok...
متن کاملFrom infinite urn schemes to decompositions of self-similar Gaussian processes
We investigate a special case of infinite urn schemes first considered by Karlin (1967), especially its occupancy and odd-occupancy processes. We first propose a natural randomization of these two processes and their decompositions. We then establish functional central limit theorems, showing that each randomized process and its components converge jointly to a decomposition of a certain self-s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008