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The quadratic covariation of Brownian motion and poisson process

  1. Jun 24, 2010 #1
    I want to know the quadratic covariation of Brownian motion B(t) and poisson process N(t).Is it B(t)?
    Thanks !
  2. jcsd
  3. Jun 24, 2010 #2
    I think it should be zero because Brownian motion is a continuous process without jump components while Poisson is a quadratic pure jump process with continuous part being constant. Hence, [tex] [B,N] = [B,N]^{c} + \Delta B \Delta N = 0 + 0 = 0 [/tex] where [tex] [B,N]^{c} [/tex] is the continuous part of quadratic covariation process.
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