scholarly journals Exponents, Symmetry Groups and Classification of Operator Fractional Brownian Motions

2011 ◽  
Vol 25 (2) ◽  
pp. 353-395 ◽  
Author(s):  
Gustavo Didier ◽  
Vladas Pipiras
Keyword(s):  
Symmetry Groups ◽  
Brownian Motions ◽  
Fractional Brownian Motions

scholarly journals On the structure and representations of max-stable processes

2010 ◽  
Vol 42 (03) ◽  
pp. 855-877 ◽  
Author(s):  
Yizao Wang ◽  
Stilian A. Stoev
Keyword(s):  
Stationary Processes ◽  
Stable Processes ◽  
Spectral Functions ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
General Classification ◽  
Classification Strategy ◽  
Spectral Representations ◽  
Linear Isometries

We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles. We propose a general classification strategy for measurable max-stable processes based on the notion of co-spectral functions. In particular, we discuss the spectrally continuous-discrete, the conservative-dissipative, and the positive-null decompositions. For stationary max-stable processes, the latter two decompositions arise from connections to nonsingular flows and are closely related to the classification of stationary sum-stable processes. The interplay between the introduced decompositions of max-stable processes is further explored. As an example, the Brown-Resnick stationary processes, driven by fractional Brownian motions, are shown to be dissipative.

scholarly journals On the structure and representations of max-stable processes

2010 ◽  
Vol 42 (3) ◽  
pp. 855-877 ◽  
Author(s):  
Yizao Wang ◽  
Stilian A. Stoev
Keyword(s):  
Stationary Processes ◽  
Stable Processes ◽  
Spectral Functions ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
General Classification ◽  
Classification Strategy ◽  
Spectral Representations ◽  
Linear Isometries

We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles. We propose a general classification strategy for measurable max-stable processes based on the notion of co-spectral functions. In particular, we discuss the spectrally continuous-discrete, the conservative-dissipative, and the positive-null decompositions. For stationary max-stable processes, the latter two decompositions arise from connections to nonsingular flows and are closely related to the classification of stationary sum-stable processes. The interplay between the introduced decompositions of max-stable processes is further explored. As an example, the Brown-Resnick stationary processes, driven by fractional Brownian motions, are shown to be dissipative.

scholarly journals Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Elhoussain Arhrrabi ◽  
M’hamed Elomari ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Stability Of Solutions ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Existence And Stability ◽  
Fractional Stochastic Differential Equations

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

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