Stage-Dependent Multiplicative Processes

2007 ◽  
pp. 181-193
Keyword(s):  
Multiplicative Processes

MULTIPLICATIVE PROCESSES OF MULTIPARTICLE PRODUCTION AND LOGARITHMIC MOMENTS

1990 ◽  
Vol 05 (04) ◽  
pp. 281-284
Author(s):  
I.M. DREMIN
Keyword(s):  
Branching Process ◽  
Multiparticle Production ◽  
Factorial Moments ◽  
Logarithmic Moments ◽  
Multiplicative Processes

The study of the dependence of the logarithmic moments on the rapidity bin width is advocated. It provides the typical details of the ensemble while usual (or factorial) moments are dominated by several rare configurations in it if multiparticle production is treated as a branching process.

Continuous, quantized and modal variation

1960 ◽  
Vol 152 (948) ◽  
pp. 397-409 ◽  
Keyword(s):  
Developmental Process ◽  
Field Size ◽  
Counting Processes ◽  
Continuous Variables ◽  
Modal Number ◽  
Integral Number ◽  
Modal Variation ◽  
Animal Populations ◽  
Almost All ◽  
Multiplicative Processes

Intraspecific variation may be continuous, or it may be quantized, if the number of structures present is always an integer. If there is some modal number of structures present in almost all individuals, variation is said to be modal. A developmental process is defined as one of ‘simple quantization’ if, first, it gives rise to an integral number of structures, and secondly, if the number of structures formed depends on the ratio between two continuous variables, for example the field size and the chemical wavelength in the model suggested by Turing (1952). Whether variation is quantized or modal will then depend on the accuracy with which these continuous variables are regulated. The larger the modal number, the more accurate must this regulation be. Data on the range of continuous variation within animal populations sug­gest that simple quantization cannot give rise to modal numbers greater than about 5 to 7. Yet modal numbers of 30 or more occur. Three processes which might account for this dis­crepancy are suggested, and evidence is presented to show that two of them occur. These are ‘multiplicative’ processes, involving successive processes of simple quantization, and ‘chemical counting’ processes, depending on qualitative differences between successively formed structures. The relevance of processes of quantization to the genesis of two-dimensional patterns is discussed.

Generalised scale invariance and multiplicative processes in the atmosphere

1989 ◽  
Vol 130 (1) ◽  
pp. 57-81 ◽  
Author(s):  
D. Schertzer ◽  
S. Lovejoy
Keyword(s):  
Scale Invariance ◽  
Multiplicative Processes

Multiplicative processes

1971 ◽  
Vol 12 (3-4) ◽  
pp. 261-272 ◽  
Author(s):  
Lloyd Demetrius
Keyword(s):  
Multiplicative Processes

Harmonic analysis for a class of multiplicative processes

1987 ◽  
Vol 33 (1) ◽  
pp. 16-20
Author(s):  
N. Weiss ◽  
K. Peterson
Keyword(s):  
Harmonic Analysis ◽  
Multiplicative Processes

scholarly journals UNCERTAINTY IN THE FLUCTUATIONS OF THE PRICE OF STOCKS

2007 ◽  
Vol 18 (11) ◽  
pp. 1689-1697 ◽  
Author(s):  
G. R. JAFARI ◽  
M. SADEGH MOVAHED ◽  
P. NOROUZZADEH ◽  
A. BAHRAMINASAB ◽  
MUHAMMAD SAHIMI ◽  
...  
Keyword(s):  
Stock Prices ◽  
Emerging Market ◽  
Critical Time ◽  
Gaussian Probability Density Function ◽  
Political Crises ◽  
Time Period ◽  
Non Gaussian ◽  
Large Increments ◽  
Probability Density Function Pdf ◽  
Multiplicative Processes

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stock prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.

Generalized vector multiplicative cascades

2001 ◽  
Vol 33 (4) ◽  
pp. 874-895 ◽  
Author(s):  
Julien Barral
Keyword(s):  
Banach Algebras ◽  
Branching Random Walk ◽  
Similar Measure ◽  
Algebra Of Functions ◽  
Convergence Results ◽  
Abstract Approach ◽  
Self Similar ◽  
Convergence Almost Surely ◽  
Varying Environment ◽  
Multiplicative Processes

We define the extension of the so-called ‘martingales in the branching random walk’ in R or C to some Banach algebras B of infinite dimension and give conditions for their convergence, almost surely and in the Lp norm. This abstract approach gives conditions for the simultaneous convergence of uncountable families of such martingales constructed simultaneously in C, the idea being to consider such a family as a function-valued martingale in a Banach algebra of functions. The approach is an alternative to those of Biggins (1989), (1992) and Barral (2000), and it applies to a class of families to which the previous approach did not. We also give a result on the continuity of these multiplicative processes. Our results extend to a varying environment version of the usual construction: instead of attaching i.i.d. copies of a given random vector to the nodes of the tree ∪n≥0N+n, the distribution of the vector depends on the node in the multiplicative cascade. In this context, when B=R and in the nonnegative case, we generalize the measure on the boundary of the tree usually related to the construction; then we evaluate the dimension of this nonstatistically self-similar measure. In the self-similar case, our convergence results make it possible to simultaneously define uncountable families of such measures, and then to estimate their dimension simultaneously.

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