A Construction of Non-Gaussian White Noise Analysis using the Theory of Hypercomplex Systems

1
M. Zakarya
M. Zakarya
2
A. S. Okb El Bab
A. S. Okb El Bab
3
Hossam A. Ghany
Hossam A. Ghany
1 Al-Azhar University-Egypt
3 Helwan University

Send Message

To: Author

GJSFR Volume 16 Issue F1

Article Fingerprint

ReserarchID

U4C9J

A Construction of Non-Gaussian White Noise Analysis using the Theory of Hypercomplex Systems Banner
  • English
  • Afrikaans
  • Albanian
  • Amharic
  • Arabic
  • Armenian
  • Azerbaijani
  • Basque
  • Belarusian
  • Bengali
  • Bosnian
  • Bulgarian
  • Catalan
  • Cebuano
  • Chichewa
  • Chinese (Simplified)
  • Chinese (Traditional)
  • Corsican
  • Croatian
  • Czech
  • Danish
  • Dutch
  • Esperanto
  • Estonian
  • Filipino
  • Finnish
  • French
  • Frisian
  • Galician
  • Georgian
  • German
  • Greek
  • Gujarati
  • Haitian Creole
  • Hausa
  • Hawaiian
  • Hebrew
  • Hindi
  • Hmong
  • Hungarian
  • Icelandic
  • Igbo
  • Indonesian
  • Irish
  • Italian
  • Japanese
  • Javanese
  • Kannada
  • Kazakh
  • Khmer
  • Korean
  • Kurdish (Kurmanji)
  • Kyrgyz
  • Lao
  • Latin
  • Latvian
  • Lithuanian
  • Luxembourgish
  • Macedonian
  • Malagasy
  • Malay
  • Malayalam
  • Maltese
  • Maori
  • Marathi
  • Mongolian
  • Myanmar (Burmese)
  • Nepali
  • Norwegian
  • Pashto
  • Persian
  • Polish
  • Portuguese
  • Punjabi
  • Romanian
  • Russian
  • Samoan
  • Scots Gaelic
  • Serbian
  • Sesotho
  • Shona
  • Sindhi
  • Sinhala
  • Slovak
  • Slovenian
  • Somali
  • Spanish
  • Sundanese
  • Swahili
  • Swedish
  • Tajik
  • Tamil
  • Telugu
  • Thai
  • Turkish
  • Ukrainian
  • Urdu
  • Uzbek
  • Vietnamese
  • Welsh
  • Xhosa
  • Yiddish
  • Yoruba
  • Zulu

In this paper, we present a generalization of white noise analysis to the case of non-Gaussian measures. For this purpose, we use a biorthogonal approach in which instead of the exponentials the characters of commutative hypercomplex systems are employed. Moreover, we construct the elements of Wick calculus in a non-Gaussian setting.

39 Cites in Articles

References

  1. S Albeverio,Yu Kondratiev,L Streit (1991). How to generalize white noise analysis to non-Gaussian measures.
  2. S Albeverio,Yu. Daletsky,Yu. Kondratiev,L Streit (1996). Non-Gaussian Infinite Dimensional Analysis.
  3. M Yu,Yu Berezansky,Samoilenko (1973). Nuclear spaces of functions of an infinite number of variables.
  4. M Yu,Yu Berezansky,Kondratiev (1995). Spectral methods in infinite dimensional analysis.
  5. M Yu,A Berezansky,Kalyuzhnyi (1992). Harmonic Analysis in Hypercomplex Systems.
  6. M Yu,Berezansky (1996). A generalization of white noise analysis by means of theory of hypergroups.
  7. M Yu,Berezansky (1991). Spectral approach to white noise analysis.
  8. M Yu,Yu Berezansky,Kondratiev (1996). Biorthogonal systems in hypergroups: an extension of non-Gaussian analysis.
  9. M Yu,A Berezansky,Kalyuzhnyi (1992). Harmonic Analysis in Hypercomplex Systems.
  10. W Bloom,H Heyer (1994). Harmonic Analysis of Probability Measures on Hypergroups.
  11. R Dobrushin,R Minlos (1977). POLYNOMIALS IN LINEAR RANDOM FUNCTIONS.
  12. L Yu,Daletsky (1991). A biorthogonal analogy of the Hermite polynomials and the inversion of the Fourier transform with respect to a non-Gaussian measure.
  13. J Delsarte (1938). Sur certaines transformation fonctionelles relative aux equations linearies aux derivees partiels du seconde ordre.
  14. Robert Elliott,John Van Der Hoek (2003). A General Fractional White Noise Theory And Applications To Finance.
  15. Hossam Ghany,Abd-Allah Hyder (2014). Abundant solutions of Wick-type stochastic fractional 2D KdV equations.
  16. Hossam Ghany,Abd-Allah Hyder (2014). Abundant solutions of Wick-type stochastic fractional 2D KdV equations.
  17. Hossam Ghany,M Zakarya (2014). Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation.
  18. H Ghany,M Zakarya (2014). Exact Solutions for Wick-type Stochastic Coupled KdV Equations.
  19. Hossam Ghany,M Zakarya (2014). Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation.
  20. Hossam Ghany,Hussain Hussain (2015). Local and global well-posedness of stochastic Kadomtsev-Petviashvili (KP) equation.
  21. Takeyuki Hida,Nobuyuki Ikeda (1965). ANALYSIS ON HILBERT SPACE WITH REPRODUCING KERNEL ARISING FROM MULTIPLE WIENER INTEGRAL.
  22. T Hida (1975). Analysis of Brownian functionals.
  23. Takeyuki Hida,Hui-Hsiung Kuo,Jürgen Potthoff,Ludwig Streit (1993). Calculus of Differential Operators.
  24. H Holden,B Osendal,J Uboe,T Zhang (2010). Stochastic partial differential equations.
  25. H-H Kuo (2002). White noise theory, Handbook of Stochastic Analysis and Applications.
  26. T Lindstrøm,B Øksendal,J Ubøe (1991). Stochastic differential equations involving positive noise.
  27. A Kalyuzhnyi (1983). Existence theorem for multiplicative measures.
  28. B Levitan (1945). Generalization of translation operation and infinite-dimensional hypercomplex systems.
  29. B Levitan (1949). Application of generalized translation operators to linear differential equations of the second order.
  30. B Levitan (1961). Lie theorems for generalized translation operators.
  31. B Levitan (1962). Generalized translation operators and some their applications.
  32. B Levitan (1973). Lie theorems for generalized translation operators.
  33. Yuta Okumura,Kenji Kashima,Yoshito Ohta (2016). Path integral approach to stochastic optimal control under non-Gaussian white noise.
  34. A Zabel,Buthinah Bin,Dehaish (2006). Negative definite functions on hypercomplex systems.
  35. A Zabel,Buthinah Bin,Dehaish (2008). L´evy Khinchin formula on commutative hypercomplex system.
  36. A Okb El Bab,A Zabel,H Ghany (2012). Harmonic analysis in Hypercomplex systems.
  37. G Us (1995). Dual Appel systems in Poissonian analysis.
  38. G Wick (1950). The Evaluation of the Collision Matrix.
  39. G Litvinov (1978). On generalized translation operators and their representations.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

M. Zakarya. 2016. \u201cA Construction of Non-Gaussian White Noise Analysis using the Theory of Hypercomplex Systems\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 16 (GJSFR Volume 16 Issue F1): .

Download Citation

Issue Cover
GJSFR Volume 16 Issue F1
Pg. 11- 25
Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords
Classification
GJSFR-F Classification: MSC 2010: 30G35
Version of record

v1.2

Issue date

February 23, 2016

Language

English

Experiance in AR

The methods for personal identification and authentication are no exception.

Read in 3D

The methods for personal identification and authentication are no exception.

Article Matrices
Total Views: 3886
Total Downloads: 1987
2026 Trends
Research Identity (RIN)
Related Research

Published Article

In this paper, we present a generalization of white noise analysis to the case of non-Gaussian measures. For this purpose, we use a biorthogonal approach in which instead of the exponentials the characters of commutative hypercomplex systems are employed. Moreover, we construct the elements of Wick calculus in a non-Gaussian setting.

Our website is actively being updated, and changes may occur frequently. Please clear your browser cache if needed. For feedback or error reporting, please email [email protected]
×

This Page is Under Development

We are currently updating this article page for a better experience.

Request Access

Please fill out the form below to request access to this research paper. Your request will be reviewed by the editorial or author team.
X

Quote and Order Details

Contact Person

Invoice Address

Notes or Comments

This is the heading

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.

High-quality academic research articles on global topics and journals.

A Construction of Non-Gaussian White Noise Analysis using the Theory of Hypercomplex Systems

A. S. Okb El Bab
A. S. Okb El Bab
Hossam A. Ghany
Hossam A. Ghany Helwan University
M. Zakarya
M. Zakarya Al-Azhar University-Egypt

Research Journals