Hypercomplex Systems with Some Applications of White Noise Analysis

M. Zakarya

ISBN 10: 620207650X / ISBN 13: 9786202076500

Verlag: LAP LAMBERT Academic Publishing, 2017

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - Applied functional analysis has many applications in other branches of mathematics, such as differential equations, numerical analysis, stochastic calculus, calculus of variations, quantum field theory, etc. Among of these applications, we interest in stochastic differential equations (SDEs). There were many authors studied this subject. Recently, Okb El Bab, Zabel, Bin Dehaish, Ghany, Hyder and Zakarya studied some important subjects related to the connection between the Harmonic analysis in hypercomplex systems (HCSs) and Gaussian calculu. So the main objective of this thesis is to use a round applied functional analysis. We gave a constructions of non-Gaussian white noise analysis (WNA) using the theory of HCSs. We introduced an elements of non-Gaussian Wick calculus based on HCSs. We applied this construction to find non-Gaussian white noise functional solutions (WNFSs) of stochastic partial differential equations (SPDEs). The KdV equation is one of the essential nonlinear equations in mathematical physics. So, we can get non-Gaussian (WNFSs) of stochastic KdV and coupled KdV equations.

Bestandsnummer des Verkäufers 9786202076500

Bibliografische Details

• Titel: Hypercomplex Systems with Some Applications of White Noise Analysis
• Verlag: LAP LAMBERT Academic Publishing
• Erscheinungsjahr: 2017
• Sprache: Englisch
• ISBN-10: 620207650X
• ISBN-13: 9786202076500
• Einband: Taschenbuch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

Applied functional analysis has many applications in other branches of mathematics, such as differential equations, numerical analysis, stochastic calculus, calculus of variations, quantum field theory, etc. Among of these applications, we interest in stochastic differential equations (SDEs). There were many authors studied this subject. Recently, Okb El Bab, Zabel, Bin Dehaish, Ghany, Hyder and Zakarya studied some important subjects related to the connection between the Harmonic analysis in hypercomplex systems (HCSs) and Gaussian calculu. So the main objective of this thesis is to use a round applied functional analysis. We gave a constructions of non-Gaussian white noise analysis (WNA) using the theory of HCSs. We introduced an elements of non-Gaussian Wick calculus based on HCSs. We applied this construction to find non-Gaussian white noise functional solutions (WNFSs) of stochastic partial differential equations (SPDEs). The KdV equation is one of the essential nonlinear equations in mathematical physics. So, we can get non-Gaussian (WNFSs) of stochastic KdV and coupled KdV equations.

Über die Autorin bzw. den Autor

Dr. M. Zakarya. He is Lecturer in Department of Mathematics, Al-Azher University, Assiut, Egypt. He is a member of the Egyptian mathematical society, a member of the Egyptian syndicate of scientific professions (2006-now). He has published research articles in reputed international journals of mathematical and mathematical physics.