Moments of Markovian growth-collapse processes

• المؤلف الرئيسي: Privault, Nicolas
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2022
• الموضوعات: Science::Mathematics; Growth–Collapse Processes; Poisson Shot Noise
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/163719
• المؤسسة: Nanyang Technological University

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.