Location of the travelling wave for the Kolmogorov equation

Maury Bramson

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Under appropriate initial data, solutions of the Kolmogorov equation {Mathematical expression} converge to travelling waves wλ(x), λ≧21/2, as t→∞. In the case λ>21/2, a general formula for the asymptotic position of the wave is known, as are formulas for certain cases of λ=21/2. The general formula for the case λ=21/2 given in [4] involves the behavior of the solution at earlier times and is typically not explicit enough for computation. Here, we give an improvement of this formula not requiring such information. The methodology involves use of sample path estimates for Brownian bridge and manipulation of certain formulas from [4].

Original languageEnglish (US)
Pages (from-to)481-515
Number of pages35
JournalProbability Theory and Related Fields
Volume73
Issue number4
DOIs
StatePublished - Nov 1 1986

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