Moments of Markovian growth-collapse processes
We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the literature to closed-form moment expressions of all orders. In co...
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sg-ntu-dr.10356-1637192022-12-15T01:17:39Z Moments of Markovian growth-collapse processes Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Growth–Collapse Processes Poisson Shot Noise We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the literature to closed-form moment expressions of all orders. In comparison with other methods based on differential equations, our approach yields explicit summations in terms of the time parameter. We also treat the case of the associated embedded chain, and provide recursive codes in Maple and Mathematica for the computation of moments and cumulants of any order with arbitrary cut-off moment sequences and jump size functions. 2022-12-15T01:17:39Z 2022-12-15T01:17:39Z 2022 Journal Article Privault, N. (2022). Moments of Markovian growth-collapse processes. Advances in Applied Probability, 54(4), 1070-1093. https://dx.doi.org/10.1017/apr.2021.63 0001-8678 https://hdl.handle.net/10356/163719 10.1017/apr.2021.63 2-s2.0-85141915058 4 54 1070 1093 en Advances in Applied Probability © 2022 The Author(s). Published by Cambridge University Press on behalf of Applied Probability Trust. All rights reserved. |
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Science::Mathematics Growth–Collapse Processes Poisson Shot Noise Privault, Nicolas Moments of Markovian growth-collapse processes |
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We apply general moment identities for Poisson stochastic integrals with random integrands to the computation of the moments of Markovian growth-collapse processes. This extends existing formulas for mean and variance available in the literature to closed-form moment expressions of all orders. In comparison with other methods based on differential equations, our approach yields explicit summations in terms of the time parameter. We also treat the case of the associated embedded chain, and provide recursive codes in Maple and Mathematica for the computation of moments and cumulants of any order with arbitrary cut-off moment sequences and jump size functions. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Privault, Nicolas |
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Privault, Nicolas |
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Moments of Markovian growth-collapse processes |
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Moments of Markovian growth-collapse processes |
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Moments of Markovian growth-collapse processes |
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Moments of Markovian growth-collapse processes |
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Moments of Markovian growth-collapse processes |
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moments of markovian growth-collapse processes |
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2022 |
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https://hdl.handle.net/10356/163719 |
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