Resolvent Cauchy and maximal estimates

Compact Doob and occupation Cauchy estimates, a fast approximation sequence, almost sure locally uniform convergence to its adapted raw limsup, and full-filter compact square-mean convergence and square integrability of the auxiliary clock at each fixed time.

Main results

• occupationDiffMartingale: the resolvent difference martingale, with its Doob bound
• integral_sq_compactError_le: explicit compact square-mean error estimate
• supOccupation_compact_L2_cauchy: compact-time Cauchy estimate
• supAuxEps: the fast approximation sequence
• ae_tendsto_supOccupation_supAuxEps_uniform: almost sure locally uniform convergence
• supAuxLimit, ae_supAuxLimit_spec: the limit and its almost sure properties
• integrable_sq_supAuxLimit: square integrability of the limit at each fixed time
• supOccupation_compact_L2_tendsto_supAuxLimit: compact square-mean convergence to the limit

References

• [J. Bertoin, Lévy Processes, Cambridge University Press, 1996, Chapters IV and VI]
• [R. M. Blumenthal and R. K. Getoor, Markov Processes and Potential Theory, Academic Press, 1968, Chapter V]