Related papers: Affine processes on $\mathbb{R}_+^n \times \mathbb…
In a recent work Sideris constructed a finite-parameter family of compactly supported affine solutions to the three-dimensional isentropic compressible Euler equations satisfying the physical vacuum condition. The support of these solutions…
We derive a necessary and sufficient condition for stochastic processes to have almost periodic finite dimensional distributions; in particular, we obtain characterizations for infinitely divisible processes to be almost periodic in terms…
In this paper we consider the existence of weakly c\`adl\`ag versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type…
Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…
This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\times d$-matrices. In particular, for conservative and subcritical affine processes on this cone we show…
The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In…
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess…
This work concerns the Ornstein-Uhlenbeck type process associated to a positive self-similar Markov process $(X(t))_{t\geq 0}$ which drifts to $\infty$, namely $U(t):= {\rm e}^{-t}X({\rm e}^t-1)$. We point out that $U$ is always a…
L\'evy-driven Ornstein-Uhlenbeck (OU) processes represent an intriguing class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current…
This article deals with IDT processes, i.e. processes which are infinitely divisible with respect to time. Given an IDT process $(X_{t},\,t\geq0)$, there exists a unique (in law) L\'evy process $(L_{t}; t\geq0)$ which has the same…
Based on a version of Dudley's Wiener process on the mass shell in the momentum Minkowski space of a massive point particle, a model of a relativistic Ornstein--Uhlenbeck process is constructed by addition of a specific drift term. The…
We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of…
We investigate the existence of affine realizations for term structure models driven by L\'evy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is…
Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…
The aim of this short note is to present the notion of IDT processes, which is a wide generalization of L\'{e}vy processes obtained from a modified infinitely divisible property. Special attention is put on a number of examples, in order to…
This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we…
We characterize various forms of positive dependence for a general class of time-inhomogeneous Markov processes called Feller evolution processes (FEPs) and for jump-FEPs. General FEPs can be studied through their time and state-space…
In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…