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Discovery Projects - Grant ID: DP160104737

Title
Discovery Projects - Grant ID: DP160104737
Funding
ARC | Discovery Projects
Contract (GA) number
DP160104737
Start Date
2016/01/01
End Date
2020/12/31
Open Access mandate
no
Organizations
-
More information
http://purl.org/au-research/grants/arc/DP160104737

 

  • Calibration for Weak Variance-Alpha-Gamma Processes

    Buchmann, Boris; Lu, Kevin W.; Madan, Dilip B. (2018)
    Projects: ARC | Discovery Projects - Grant ID: DP160104737 (DP160104737)
    The weak variance-alpha-gamma process is a multivariate L\'evy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibration methods for the weak variance-alpha-gamma process, method of moments, maximum likelihood estimation (MLE) and digital moment estimation (DME). We derive a condition for Fou...

    Selfdecomposability of Variance Generalised Gamma Convolutions

    Buchmann, Boris; Lu, Kevin W.; Madan, Dilip B. (2017)
    Projects: ARC | Discovery Projects - Grant ID: DP160104737 (DP160104737)
    Variance generalised gamma convolution processes are multivariate Brownian motions weakly subordinated by multivariate Thorin subordinators. Within this class, we show that a drift-less Brownian motion gives rise to a self-decomposable process. Under a moment condition on the underlying Thorin measure, we show that this condition is also necessary. Our conditions generalises earlier results relating to self-decomposability when the Thorin subordinator has indistinguisdhable components. We app...

    Processes of rth Largest

    For integers $n\geq r$, we treat the $r$th largest of a sample of size $n$ as an $\mathbb{R}^\infty$-valued stochastic process in $r$ which we denote $\mathbf{M}^{(r)}$. We show that the sequence regarded in this way satisfies the Markov property. We go on to study the asymptotic behaviour of $\mathbf{M}^{(r)}$ as $r\to\infty$, and, borrowing from classical extreme value theory, show that left-tail domain of attraction conditions on the underlying distribution of the sample guarantee weak lim...

    Trimmed L\'evy Processes and their Extremal Components

    We analyse a trimmed stochastic process of the form ${}^{(r)}X_t= X_t - \sum_{i=1}^r \Delta_t^{(i)}$, where $(X_t)_{t \geq 0}$ is a driftless subordinator on $\mathbb{R}$ with its jumps on $[0,t]$ ordered as $ \Delta_t^{(1)}\ge \Delta_t^{(2)} \cdots$. When $r\to\infty$, both ${}^{(r)}X_t \to 0$ and $\Delta_t^{(r)} \to 0$ a.s. for each $t>0$, and it is interesting to study the weak limiting behaviour of $\bigl({}^{(r)}X_t, \Delta_t^{(r)}\bigr)$ in this case. We term this "large-trimming" behav...
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