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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Cadlag modification

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums - The Fusion of Science and Community**