Stochastic Evolution Equations Driven by Fractional Noises

Abstract

We have introduced a modification of the classical Euler numerical scheme for stochastic differential equations driven by a fractional Brownian motion with Hurst parameter larger than 1/2. For this new scheme, we have derived a precise rate of convergence to zero or the error and the limit in distribution of the error fluctuations. We have studied time discrete numerical schemes based on Taylor expansions for rough differential equations and for stochastic differential equations driven by a fractional Brownian motion with Hurst parameter larger than 1/2.

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Document Details

Document Type
Technical Report
Publication Date
Nov 28, 2016
Accession Number
AD1037543

Entities

People

  • David Nualart

Organizations

  • University of Kansas

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Calculus
  • Data Science
  • Differential Equations
  • Equations
  • Gaussian Noise
  • Gaussian Processes
  • Information Science
  • Integrals
  • Partial Differential Equations
  • Probability
  • Random Variables
  • Real Numbers
  • Standards
  • Stochastic Processes
  • Students
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Control Systems Engineering.
  • Wave Propagation and Nonlinear Chaotic Dynamics.