Abstract Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their transition laws are linked properties what will be hereafter called -remainder self-decomposable stationary laws. present study we fully characterize Lévy triplet these $$a$$ a</mml:...

Abstract There are two types of tempered stable (TS) based Ornstein–Uhlenbeck (OU) processes: (i) the OU-TS process , OU driven by a TS subordinator, and (ii) TS-OU with marginal law. They have various applications in financial engineering econometrics. In literature, only second type under stationary assumption has an exact simulation algorithm. this paper we develop unified approach to exactl...

We give a description, in terms of “pseudo-stable increasing process”, of the Lamperti process associated with the inverse local time of a radial Ornstein-Uhlenbeck process. Following Bertoin-Yor, we also express, in two particular cases, the law of the perpetuity associated with this inverse local time.

We present a stochastic volatility market model where volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. With this model we exactly measure the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the p...

We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.

In this work we investigate semigroups of operators acting on noncommutative L-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, q-Ornstein-Uhlenbeck semigroups, and the noncommutative Poiss...