Constructing the fractional Brownian motion Mohamed Ndaoud - - PowerPoint PPT Presentation

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constructing the fractional brownian motion
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Constructing the fractional Brownian motion Mohamed Ndaoud - - PowerPoint PPT Presentation

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Constructing the fractional Brownian motion Mohamed Ndaoud Department of Statistics CREST, Paris 11 Mai 2017 Les probabilits de demain IHS Outline Introduction Defjnition Application of fBm Real data Simulated data

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Constructing the fractional Brownian motion

  • Mohamed Ndaoud
  • Department of Statistics
  • CREST, Paris

11 Mai 2017 Les probabilités de demain IHÉS

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SLIDE 2

Outline

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SLIDE 3

Introduction

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SLIDE 4

Defjnition

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Application of fBm

Real data Simulated data

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Simulation of fBm

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SLIDE 7

Series expansion for continuous stochastic processes

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Defjnition

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Mercer’s theorem

Theorem:

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Karhunen-Loève theorem

Theorem:

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Sketch of the proof

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Constructing the fractional Brownian motion

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Constructing fBm

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Constructing fBm

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Fourier spectrum of the fractional Kernel

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Constructing fBm

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The series expansion

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Simulation of fBm

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Previous expansions

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Conclusion

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Conclusion

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Thank you for your attention!