One more square root law for Brownian motion and its application to SPDEs

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Abstract

It is proved that there is a function p(c) ≥ 0 such that p(c) > 0 if c is large enough, and (a.s.) for any t ∈ [0, 1], the trajectory of Brownian motion after time t is contained in a parallel shift of the box [0, 2-k] × [0, c2-k/2] for all k belonging to a set with lower density ≥ p(c). This law of square root helps show that solutions of one-dimensional SPDEs are Hölder continuous up to the boundary.

Original languageEnglish (US)
Pages (from-to)496-512
Number of pages17
JournalProbability Theory and Related Fields
Volume127
Issue number4
DOIs
StatePublished - Dec 1 2003

Keywords

  • Brownian motion
  • Square root law
  • Stochastic partial differential equations

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