Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference
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A01=Ciprian A Tudor
Author_Ciprian A Tudor
Category=PBWL
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eq_nobargain
Fractional and Bifractional Brownian Motion
Gaussian Processes
Gaussian Random Noise
Parameter Estimation
Power Variation
Stochastic Heat Equation
Stochastics Wave Equation
Product details
- ISBN 9789811264450
- Publication Date: 24 Nov 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
