ORCID Profile
0000-0003-1710-7747
Current Organisation
University of Adelaide
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Publisher: Informa UK Limited
Date: 29-06-2018
Publisher: Elsevier BV
Date: 10-2020
Publisher: Elsevier BV
Date: 09-2022
Publisher: Cambridge University Press (CUP)
Date: 20-09-2023
DOI: 10.1017/JPR.2022.25
Abstract: Let f be the density function associated to a matrix-exponential distribution of parameters $(\\boldsymbol{\\alpha}, T,\\boldsymbol{{s}})$ . By exponentially tilting f , we find a probabilistic interpretation which generalizes the one associated to phase-type distributions. More specifically, we show that for any sufficiently large $\\lambda\\ge 0$ , the function $x\\mapsto \\left(\\int_0^\\infty e^{-\\lambda s}f(s)\\textrm{d} s\\right)^{-1}e^{-\\lambda x}f(x)$ can be described in terms of a finite-state Markov jump process whose generator is tied to T . Finally, we show how to revert the exponential tilting in order to assign a probabilistic interpretation to f itself.
Publisher: Elsevier BV
Date: 2018
Publisher: Cambridge University Press (CUP)
Date: 18-01-2022
DOI: 10.1017/JPR.2021.30
Abstract: Latouche and Nguyen (2015b) constructed a sequence of stochastic fluid processes and showed that it converges weakly to a Markov-modulated Brownian motion (MMBM). Here, we construct a different sequence of stochastic fluid processes and show that it converges strongly to an MMBM. To the best of our knowledge, this is the first result on strong convergence to a Markov-modulated Brownian motion. Besides implying weak convergence, such a strong approximation constitutes a powerful tool for developing deep results for sophisticated models. Additionally, we prove that the rate of this almost sure convergence is $o(n^{-1/2} \\log n)$ . When reduced to the special case of standard Brownian motion, our convergence rate is an improvement over that obtained by a different approximation in Gorostiza and Griego (1980), which is $o(n^{-1/2}(\\log n)^{5/2})$ .
Publisher: Elsevier BV
Date: 07-2022
No related grants have been discovered for Oscar Peralta Gutierrez.