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Random walk models

Random walk models

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In this chapter we have considered a class of models that complement and illuminate the compound form of the K process discussed in Chapter 6. These models have in the main grown out of the optics literature, and tend to highlight the role played by individual scatterers, rather than a speckle process modulated by the partially resolved structure of the sea surface. Consequently, they provide a useful vehicle for the discussion of sea spikes and bursts generated by breaking waves; this analysis allows us to draw together the K, Class A and BEMs into a consistent whole. The formulation of the K process in terms of FP and SDEs has also been discussed; the impetus lent to this methodology by its application in financial modelling and other areas may yet result in this formulation being of practical as well as academic interest.

Chapter Contents:

  • 7.1 Introduction
  • 7.2 A random walk model of non-Gaussian scattering
  • 7.3 The Class A and breaking area models
  • 7.4 A Fokker-Planck description of K distributed noise
  • 7.5 Conclusions
  • References

Inspec keywords: random processes; Fokker-Planck equation; stochastic processes

Other keywords: breaking area model; BAM; random walk model; K process; FP; financial modelling; SDE; Fokker-Planck equation; stochastic differential equation

Subjects: Statistics; Other topics in statistics; Other topics in statistics; Probability theory, stochastic processes, and statistics

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