Abstract
We give stopped Doob inequalities for p-th moment, 0<p<∞, of stochastic convolution integrals ∫(0,t] U(t,s)φ s − dM s in a Hilbert space, where M is a Hilbert space-valued cadlag square integrable martingale, φ is an operator-valued predictable process and U(t,s) is a contraction-type evolution operator. We also generalize the previous results and try to get smaller constants.
1This research was partially supported by Sharif University of Technology.
Acknowledgment
The first author is grateful to Professor N.U. Ahmed for very stimulating attention to this work.
Notes
1This research was partially supported by Sharif University of Technology.