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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Cadlag modification

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