First Crossing a Random Process

  • Shelemyahu Zacks
Part of the Lecture Notes in Mathematics book series (LNM, volume 2203)


A rendezvous time is a time at which two different stochastic processes intersect (meet). In this section we discuss the first such rendezvous time of a Brownian motion and an independent compound Poisson process. The reader is referred to Perry et al. (2004) and Che and Dassios (2013).


  1. Che, X. and Dassios, A. (2013). Stochastic boundary crossing probabilities for the Brownian motion. J. Appl. Prob., 50: 419–429.MathSciNetCrossRefMATHGoogle Scholar
  2. Perry, D., Stadje, W. and Zacks, S. (2004). The first rendezvous time of Brownian motion and compound Poisson type processes. J. Appl. Prob., 41:1059–1070.MathSciNetCrossRefMATHGoogle Scholar
  3. Perry, D., Stadje, W. and Zacks, S. (2005). A two-sided first-exit problem for compound Poisson process with a random upper boundary. Meth. Comput. Appl. Prob. 7:51–62. Google Scholar
  4. Picard, P. and Lefèvre, C. (2003). On the first meeting or crossing of two independent trajectories for some counting processes, Stochastic Processes and their Applications, 104: 217–242.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Shelemyahu Zacks
    • 1
  1. 1.Binghamton UniversityBinghamtonUSA

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