An Edgeworth expansion of a Studentized statistic for an ergodic regenerative strong Markov process is validated. A specific nonparametric bootstrap method is proposed and proved to be second-order correct in the light of the Edgeworth expansion, which is a variant of the regenerative block bootstrap designed for discrete-time Markov processes. One-dimensional diffusions and semi-Markov process...

by Magne Myrtveit Normally, we try to aggregate discreteness in System Dynamics (SD) models by making continuous flows. This is a good modeling practice, but in some cases discreteness may have a significant influence on system behavior (see note). Consequently, we need to model such discreteness to explore its impact on behavior. The System Dynamics (SD) technology was originally designed with...

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e. a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredi...

We develop a bootstrap procedure for Lévy-driven continuous-time autoregressive (CAR) processes observed at discrete regularly-spaced times. It is well known that a regularly sampled stationary Ornstein–Uhlenbeck process [i.e. a CAR(1) process] has a discrete-time autoregressive representation with i.i.d. noise. Based on this representation a simple bootstrap procedure can be found. Since regul...

In this paper we present a review on the extremal behavior of stationary continuous-time processes with emphasis on generalized Ornstein-Uhlenbeck processes. We restrict our attention to heavy-tailed models like heavy-tailed Ornstein-Uhlenbeck processes or continuous-time GARCH processes. The survey includes the tail behavior of the stationary distribution, the tail behavior of the sample maxim...

1 Basic Concepts 3 1.1 Notions of equivalence of stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Sample path properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Properties of filtrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Stopping times . . . . . . . . . . . . . . . . . ....