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Regularity of stochastic kinetic equations

Electronic Journal of Probability, ISSN: 1083-6489, Vol: 22, Issue: 0
2017
  • 24
    Citations
  • 0
    Usage
  • 4
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    24
    • Citation Indexes
      24
  • Captures
    4

Article Description

We consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity (L -regularity in the velocity-variable and Sobolev regularity in the space-variable). We prove that, in contrast with the deterministic case, the SPDE admits a unique weakly differentiable solution which preserves a certain degree of Sobolev regularity of the initial condition without developing discontinuities. To prove the result we also study the related degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a suitable stochastic flow.

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