Killed Brownian Motion

  • Kai Lai Chung
  • Zhongxin Zhao
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 312)

Abstract

Let Xt be the d-dimensional Brownian motion and D a domain in ℝd (d≥ 1). Adjoin an extra point ∂ to D and set
$$ X_t^D = \left\{ {\begin{array}{*{20}c} {X_t on (t < \tau _D )} \\ {\partial on (t \geqslant \tau _D ).} \\ \end{array} } \right. $$

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Kai Lai Chung
    • 1
  • Zhongxin Zhao
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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