Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference

Released on by Ciprian A Tudor
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  • Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference Book Detail

  • Author : Ciprian A Tudor
  • Release Date : 2022-10-11
  • Publisher : World Scientific
  • Genre : Mathematics
  • Pages : 205
  • ISBN 13 : 9811264473
  • File Size : 63,63 MB
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Stochastic Partial Differential Equations With Additive Gaussian Noise - Analysis And Inference by Ciprian A Tudor PDF Summary

Book Description: 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.

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Stochastic Partial Differential Equations

Stochastic Partial Differential Equations

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This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a g