‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

∗Preliminary Comments are welcome. Paper written for the Handbook of Financial Econometrics edited by Yacine Aı̈t-Sahalia and Lars Peter Hansen. We thank Darrell Duffie, Benoit Perron and Mark Watson for discussions and Seoyeon Lee for research assistance. Bandi acknowledges financial support from the IBM Corporation Faculty Research Fund at the University of Chicago. Phillips thanks fhe NSF for...

Overcoming the disadvantages of equidistant discretization of continuous actions, we introduce an approach that separates time into slices of varying length bordered by certain events. Such events are points in time at which the equations describing the system’s behavior—that is, the equations which specify the ongoing processes—change. Between two events the system’s parameters stay continuous...

The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self-dual processes. Moreover, we give a characterisation of continuous Ocone mar...