Classical and Generalized Solutions of Fractional Stochastic Differential Equations

Abstract

For stochastic evolution equations with fractional derivatives, classical solutions exist when the order of the time derivative of the unknown function is not too small compared to the order of the time derivative of the noise; otherwise, there can be a generalized solution in suitable weighted chaos spaces. Presence of fractional derivatives in time leads to various modifications of the stochastic parabolicity condition. Interesting new effects appear when the order of the time derivative in the noise term is less than or equal to one-half.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2018
Accession Number
AD1135443

Entities

People

  • B. L. Rozovsky
  • S. V. Lototsky

Organizations

  • Brown University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Applied Mathematics
  • Brownian Motion
  • Calculus
  • Differential Equations
  • Diffusion
  • Electronic Mail
  • Equations
  • Integral Equations
  • Integrals
  • Mathematics
  • New York
  • Noise
  • Numbers
  • Partial Differential Equations
  • Personal Information Managers
  • Probability
  • Random Variables
  • Random Walk
  • Real Numbers
  • Standards
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space