Moments of Hölder coefficients on random time intervals

We show existence of moments for Hölder coefficients up to a random time. Our result applies to general processes satisfying Kolmogorov’s tightness criterion and (unbounded) random times with a higher moment. The proof is based on a ramification of Kolmogorov’s classical dyadic numbers argument. We illustrate the result for diffusions and BSDEs on unbounded time horizons.