Additive subordination of multiparameter Markov processes

Abstract

We extend Phillips theorem to multiparameter, multidimensional Markov processes that are time-changed by an independent additive subordinator. We show that the resulting process is a Feller evolution and we characterize its generator. We further derive its pseudo-differential representation and show that its symbol admits a Levy-Khintchine representation, thereby providing analytical tractability. We then subordinate a multiparameter Ornstein-Uhlenbeck process using a multivariate Sato process and construct a multivariate asset model that accounts for both mean reversion and time inhomogeneity, allowing each asset to evolve according to its own economic time, in line with empirical evidence.

arXiv comment32 pages