scholarly journals Effects of randomness on power law tails in multiplicatively interacting stochastic processes

2004 ◽  
Vol 324 (5-6) ◽  
pp. 378-382 ◽  
Author(s):  
Toshiya Ohtsuki ◽  
Akihiro Fujihara ◽  
Hiroshi Yamamoto
Keyword(s):  
Stochastic Processes ◽  
Power Law

Power-law autocorrelated stochastic processes with long-range cross-correlations

2007 ◽  
Vol 56 (1) ◽  
pp. 47-52 ◽  
Author(s):  
B. Podobnik ◽  
D. F. Fu ◽  
H. E. Stanley ◽  
P. Ch. Ivanov
Keyword(s):  
Stochastic Processes ◽  
Long Range ◽  
Power Law ◽  
Cross Correlations

scholarly journals Multifractal products of stochastic processes: construction and some basic properties

2002 ◽  
Vol 34 (4) ◽  
pp. 888-903 ◽  
Author(s):  
Petteri Mannersalo ◽  
Ilkka Norros ◽  
Rudolf H. Riedi
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Power Law ◽  
Special Form ◽  
Multifractal Spectrum ◽  
Nonstationary Process ◽  
Limit Process ◽  
Stationary Stochastic Processes ◽  
Measured Time ◽  
Multifractal Scaling

In various fields, such as teletraffic and economics, measured time series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a nonstationary process. To overcome this problem, we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a special form of T-martingales. We study the ℒ2-convergence, nondegeneracy, and continuity of the limit process. Establishing a power law for its moments, we obtain a formula for the multifractal spectrum and hint at how to prove the full formalism.

scholarly journals Multifractal products of stochastic processes: construction and some basic properties

2002 ◽  
Vol 34 (04) ◽  
pp. 888-903 ◽  
Author(s):  
Petteri Mannersalo ◽  
Ilkka Norros ◽  
Rudolf H. Riedi
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Power Law ◽  
Special Form ◽  
Multifractal Spectrum ◽  
Nonstationary Process ◽  
Limit Process ◽  
Stationary Stochastic Processes ◽  
Measured Time ◽  
Multifractal Scaling

In various fields, such as teletraffic and economics, measured time series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a nonstationary process. To overcome this problem, we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a special form of T-martingales. We study the ℒ2-convergence, nondegeneracy, and continuity of the limit process. Establishing a power law for its moments, we obtain a formula for the multifractal spectrum and hint at how to prove the full formalism.

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