Stochastic Partial Differential Equations with Additive Gaussian Noise - Analysis and Inference

Ciprian A Tudor

ISBN 10: 9811264457 / ISBN 13: 9789811264450

Editore: World Scientific Publishing Company, 2022

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nach der Bestellung gedruckt Neuware - Printed after ordering - The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation.The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space.The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.

Codice articolo 9789811264450

Dati bibliografici

• Titolo: Stochastic Partial Differential Equations with Additive Gaussian Noise - Analysis and Inference
• Editore: World Scientific Publishing Company
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 9811264457
• ISBN 13: 9789811264450
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 235 L x 157 A x 16 P (millimetri) 235 millimetri di larghezza per 157 millimetri di altezza per 16 millimetri di profondità
• Peso: 457 grammi

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Riassunto

The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation. The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space. The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.