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Robert Stelzer

  1. Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes.

    Пт, 03/02/2012 - 15:01 — SomNambul
    Authors: Robert Stelzer, Eckhard Schlemm
    Subjects: Statistics
    Abstract

    The class of multivariate L\'{e}vy-driven autoregressive moving average
    (MCARMA) processes, the continuous-time analogs of the classical vector ARMA
    processes, is shown to be equivalent to the class of continuous-time state
    space models. The linear innovations of the weak ARMA process arising from
    sampling an MCARMA process at an equidistant grid are proved to be
    exponentially completely regular ($\beta$-mixing) under a mild continuity
    assumption on the driving L\'{e}vy process.

  2. A Class of Infinitely Divisible Multivariate and Matrix Gamma Distributions and Cone-valued Generalised Gamma Convolutions.

    Пнд, 01/09/2012 - 15:01 — SomNambul
    Authors: Robert Stelzer, Victor Pérez-Abreu
    Subjects: Probability
    Abstract

    Classes of multivariate and cone valued infinitely divisible Gamma
    distributions are introduced. Particular emphasis is put on the cone-valued
    case, due to the relevance of infinitely divisible distributions on the
    positive semi-definite matrices in applications. The cone-valued class of
    generalised Gamma convolutions is studied. In particular, a characterisation in
    terms of an It\^o-Wiener integral with respect to an infinitely divisible
    random measure associated to the jumps of a L\'evy process is established.

  3. Limit Theory for the largest eigenvalues of sample covariance matrices with heavy-tails.

    Втр, 08/30/2011 - 15:01 — SomNambul
    Authors: Robert Stelzer, Oliver Pfaffel, Richard A. Davis
    Subjects: Probability
    Abstract

    We study the joint limit distribution of the $k$ largest eigenvalues of a
    $p\times p$ sample covariance matrix $XX^\T$ based on a large $p\times n$
    matrix $X$. The rows of $X$ are given by independent copies of a linear
    process, $X_{it}=\sum_j c_j Z_{i,t-j}$, with regularly varying noise $(Z_{it})$
    with tail index $\alpha\in(0,2)$. It is shown that the point process based on
    the eigenvalues of $XX^\T$ converges in distribution to a Poisson point process
    with intensity measure depending on $\alpha$ and $\sum c_j^2$.

  4. Multivariate COGARCH(1,1) processes.

    Ср, 02/24/2010 - 16:01 — SomNambul
    Authors: Robert Stelzer
    Subjects: Statistics
    Abstract

    Multivariate $\operatorname {COGARCH}(1,1)$ processes are introduced as a
    continuous-time models for multidimensional heteroskedastic observations. Our
    model is driven by a single multivariate L\'{e}vy process and the latent
    time-varying covariance matrix is directly specified as a stochastic process in
    the positive semidefinite matrices. After defining the $\operatorname
    {COGARCH}(1,1)$ process, we analyze its probabilistic properties.

  5. Option pricing in multivariate stochastic volatility models of OU type.

    Ср, 01/20/2010 - 16:02 — SomNambul
    Authors: Robert Stelzer, Oliver Pfaffel, Johannes Muhle-Karbe
    Subjects: Pricing of Securities
    Abstract

    We present a multivariate stochastic volatility model with leverage, which is
    flexible enough to recapture the individual dynamics as well as the
    interdependencies between several assets while still being highly analytically
    tractable.

  6. On strong solutions for positive definite jump-diffusions.

    Пнд, 10/12/2009 - 10:31 — SomNambul
    Authors: Robert Stelzer, Eberhard Mayerhofer, Oliver Pfaffel
    Subjects: Probability
    Abstract

    We show the existence of unique global strong solutions of a class of
    stochastic differential equations on the cone of symmetric positive definite
    matrices. Our result includes affine diffusion processes and therefore extends
    considerably the known statements concerning Wishart processes.

  7. On strong solutions for positive definite jump-diffusions.

    Пнд, 10/12/2009 - 10:31 — SomNambul
    Authors: Robert Stelzer, Eberhard Mayerhofer, Oliver Pfaffel
    Subjects: Probability
    Abstract

    We show the existence of unique global strong solutions of a class of
    stochastic differential equations on the cone of symmetric positive definite
    matrices. Our result includes affine diffusion processes and therefore extends
    considerably the known statements concerning Wishart processes.

  8. On the definition, stationary distribution and second order structure of positive semidefinite Ornstein--Uhlenbeck type processes.

    Пнд, 09/07/2009 - 10:33 — SomNambul
    Authors: Christian Pigorsch, Robert Stelzer
    Subjects: Statistics
    Abstract

    Several important properties of positive semidefinite processes of
    Ornstein--Uhlenbeck type are analysed. It is shown that linear operators of the
    form $X\mapsto AX+XA^{\mathrm{T}}$ with $A\in M_d(\mathbb{R})$ are the only
    ones that can be used in the definition provided one demands a natural
    non-degeneracy condition.

  9. On the definition, stationary distribution and second order structure of positive semidefinite Ornstein--Uhlenbeck type processes.

    Пнд, 09/07/2009 - 10:33 — SomNambul
    Authors: Christian Pigorsch, Robert Stelzer
    Subjects: Statistics
    Abstract

    Several important properties of positive semidefinite processes of
    Ornstein--Uhlenbeck type are analysed. It is shown that linear operators of the
    form $X\mapsto AX+XA^{\mathrm{T}}$ with $A\in M_d(\mathbb{R})$ are the only
    ones that can be used in the definition provided one demands a natural
    non-degeneracy condition.

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