On a result of C. Mueller and E. Perkins

N. V. Krylov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The equation du = (au″+ bu′ + cu) dt + vuγ W(dx, dt) is considered for γ ε (0, 1). It is proved that u(t, ·) has compact support for all t ≥ 0 if u(0, ·) does. This result extends a result of C. Mueller and E. Perkins who considered the case a = 1, b = c = 0. The proof does not use the nonstandard analysis unlike the one by C. Mueller and E. Perkins.

Original languageEnglish (US)
Pages (from-to)543-557
Number of pages15
JournalProbability Theory and Related Fields
Volume108
Issue number4
DOIs
StatePublished - Aug 1997

Keywords

  • Solutions with compact support
  • Two-parameter white noise

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