Cadlag modification

  1. I was reading Stochastic Integration and Differential Equations by Protter and it had a nice theorem that every Levy process in law which has continuity in probability, admits a cadlag modification. The proof is very confusing and I was wondering if anyone could help me clear it up a bit.

    I wish to prove a slight modification, which is that the set
    [tex]\{\omega : \not \exists \lim_{\mathbb{Q}\ni s\downarrow t}X_t(\omega) \quad t \geq 0 \}[/tex]
    is measurable and has a measure zero. I have that X has stationary independent increments and is continuous in probability (also X starts at 0 a.s.). Any help would be much appreciated.
  2. jcsd
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