Abstract
Consider a càdlàg local martingale M with square brackets M . In this paper, we
provide upper and lower bounds for expectations of the type E M q/2
τ , for any
stopping time τ and q ≥ 2, in terms of predictable processes. This result can be
thought of as a Burkholder-Davis-Gundy type inequality in the sense that it can be
used to relate the expectation of the running maximum |M ∗|q to the expectation of
the dual previsible projections of the relevant powers of the associated jumps of M .
The case for a class of moderate functions is also discussed.
Users
Please
log in to take part in the discussion (add own reviews or comments).