Conditional Brownian Motion

  • J. L. Doob
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 262)


Let D be an open subset of ℝ N , and recall that a Brownian motion in D was defined in Section VII.9 as an almost surely continuous Markov process with state space D and transition density b D . The probability space on which the process is defined may or may not be rich enough to extend the process to be a Brownian motion in ℝ N .


Brownian Motion Optional Time Martin Boundary Positive Harmonic Function Finite Lifetime 
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Copyright information

© Springer-Verlag New York Inc. 1984

Authors and Affiliations

  • J. L. Doob
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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