Moduli of continuity of the local time of a class of sub-fractional Brownian motions

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Mohamed Ait Ouahra ◽  
Raby Guerbaz
Keyword(s):  
Local Time ◽  
Similarity Index ◽  
The Self ◽  
Local Times ◽  
Moduli Of Continuity ◽  
Self Similarity ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Sharp Estimates

AbstractThe aim of this paper is to establish sharp estimates for the moduli of continuity of the local time of a class of sub-fractional Brownian motions. We also investigate the continuity of their local times with respect to the self-similarity index.

Collision Local Times and Measure-Valued Processes

1991 ◽  
Vol 43 (5) ◽  
pp. 897-938 ◽  
Author(s):  
Martin T. Barlow ◽  
Steven N. Evans ◽  
Edwin A. Perkins
Keyword(s):  
Local Time ◽  
Forthcoming Paper ◽  
Local Times ◽  
Independent Interest ◽  
Positive Probability ◽  
Point Interactions ◽  
Random Measures ◽  
Brownian Motions ◽  
Collision Local Time ◽  
Finite Measures

AbstractWe consider two independent Dawson-Watanabe super-Brownian motions, Y1 and Y2. These processes are diffusions taking values in the space of finite measures on ℝd. We show that if d ≤ 5 then with positive probability there exist times t such that the closed supports of intersect; whereas if d > 5 then no such intersections occur. For the case d ≤ 5, we construct a continuous, non-decreasing measure–valued process L(Y1, Y2), the collision local time, such that the measure defined by , is concentrated on the set of times and places at which intersections occur. We give a Tanaka-like semimartingale decomposition of L(Y1, Y2). We also extend these results to a certain class of coupled measurevalued processes. This extension will be important in a forthcoming paper where we use the tools developed here to construct coupled pairs of measure-valued diffusions with point interactions. In the course of our proofs we obtain smoothness results for the random measures that are uniform in t. These theorems use a nonstandard description of Yi and are of independent interest.

DIVERGENCE RESULTS FOR SELF-INTERSECTION LOCAL TIMES OF GAUSSIAN ${\mathscr S}' ({\mathbb R}^d)$-PROCESSES

2001 ◽  
Vol 04 (04) ◽  
pp. 417-488 ◽  
Author(s):  
ANNA TALARCZYK
Keyword(s):  
Local Time ◽  
Necessary Conditions ◽  
Particle Systems ◽  
The Self ◽  
Local Times ◽  
Intersection Local Time ◽  
Convergence In Law ◽  
Stable Particle ◽  
Gaussian Formula ◽  
Intersection Local Times

For various types of Gaussian [Formula: see text]-processes we consider the case when the self-intersection local time (SILT) does not exist. We study the rate of divergence of the corresponding approximating processes obtaining, after suitable normalizations convergence in law to some [Formula: see text]-valued processes (not necessarily Gaussian). We also obtain some new necessary conditions for the existence of SILT. We give examples associated with fluctuation limits of α-stable particle systems.

scholarly journals A COMPARISON OF THREE HURST EXPONENT APPROACHES TO PREDICT NASCENT BUBBLES IN S&P500 STOCKS

Fractals ◽  
2017 ◽  
Vol 25 (01) ◽  
pp. 1750006 ◽  
Author(s):  
M. FERNÁNDEZ-MARTÍNEZ ◽  
M. A. SÁNCHEZ-GRANERO ◽  
M. J. MUÑOZ TORRECILLAS ◽  
BILL MCKELVEY
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
Price Change ◽  
Similarity Index ◽  
The Self ◽  
Stock Index ◽  
Fluctuation Analysis ◽  
Market Behavior ◽  
Self Similarity ◽  
Efficient Market

Since the pioneer contributions due to Vandewalle and Ausloos, the Hurst exponent has been applied by econophysicists as a useful indicator to deal with investment strategies when such a value is above or below [Formula: see text], the Hurst exponent of a Brownian motion. In this paper, we hypothesize that the self-similarity exponent of financial time series provides a reliable indicator for herding behavior (HB) in the following sense: if there is HB, then the higher the price, the more the people will buy. This will generate persistence in the stocks which we shall measure by their self-similarity exponents. Along this work, we shall explore whether there is some connections between the self-similarity exponent of a stock (as a HB indicator) and the stock’s future performance under the assumption that the HB will last for some time. With this aim, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which performs best to identify the transition from random efficient market behavior to HB and hence, to detect the beginning of a bubble. Generalized Hurst Exponent, Detrended Fluctuation Analysis, and GM2 algorithms have been tested. Traditionally, researchers have focused on identifying the beginning of a crash. We study the beginning of the transition from efficient market behavior to a market bubble, instead. Our empirical results support that the higher (respectively the lower) the self-similarity index, the higher (respectively the lower) the mean of the price change, and hence, the better (respectively the worse) the performance of the corresponding stock. This would imply, as a consequence, that the transition process from random efficient market to HB has started. For experimentation purposes, S&P500 stock Index constituted our main data source.

scholarly journals Hölder properties of local times for fractional Brownian motions

Metrika ◽  
2008 ◽  
Vol 69 (2-3) ◽  
pp. 125-152 ◽  
Author(s):  
D. Baraka ◽  
T. Mountford ◽  
Y. Xiao
Keyword(s):  
Local Times ◽  
Brownian Motions ◽  
Fractional Brownian Motions

scholarly journals After notes on self-similarity exponent for fractal structures

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 440-448 ◽  
Author(s):  
Manuel Fernández-Martínez ◽  
Manuel Caravaca Garratón
Keyword(s):  
Fractal Dimension ◽  
Broad Spectrum ◽  
Fractal Structure ◽  
Similarity Index ◽  
Random Processes ◽  
The Self ◽  
Sample Function ◽  
Fractal Structures ◽  
Self Similarity ◽  
Image Set

AbstractPrevious works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.

scholarly journals On the self-similarity index of 𝑝-adic analytic pro-𝑝 groups

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Francesco Noseda ◽  
Ilir Snopce
Keyword(s):  
Rooted Tree ◽  
Similarity Index ◽  
The Self ◽  
Self Similarity ◽  
Similar Action ◽  
3 Dimensional ◽  
Self Similar

Abstract Let 𝑝 be a prime. We say that a pro-𝑝 group is self-similar of index p k p^{k} if it admits a faithful self-similar action on a p k p^{k} -ary regular rooted tree such that the action is transitive on the first level. The self-similarity index of a self-similar pro-𝑝 group 𝐺 is defined to be the least power of 𝑝, say p k p^{k} , such that 𝐺 is self-similar of index p k p^{k} . We show that, for every prime p ⩾ 3 p\geqslant 3 and all integers 𝑑, there exist infinitely many pairwise non-isomorphic self-similar 3-dimensional hereditarily just-infinite uniform pro-𝑝 groups of self-similarity index greater than 𝑑. This implies that, in general, for self-similar 𝑝-adic analytic pro-𝑝 groups, one cannot bound the self-similarity index by a function that depends only on the dimension of the group.

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