Exact expression of ultimate time survival probability in homogeneous discrete-time risk model

نویسندگان

چکیده

In this work we set up the generating function of ultimate time survival probability $\varphi(u+1)$, where $$\varphi(u)=\mathbb{P}\left(\sup_{n\geqslant 1}\sum_{i=1}^{n}\left(X_i-\kappa\right)<u\right)$$ and $u\in\mathbb{N}_0,\,\kappa\in\mathbb{N}$, random walk $\left\{\sum_{i=1}^{n}X_i,\,n\in\mathbb{N}\right\}$ consists independent identically distributed variables $X_i$, which are non-negative integer valued. We also give expressions $\varphi(u)$ via roots certain polynomials. Based on proven theoretical statements, several examples its expressions, when $X_i$ admit Bernoulli, Geometric some other distributions.

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ژورنال

عنوان ژورنال: AIMS mathematics

سال: 2022

ISSN: ['2473-6988']

DOI: https://doi.org/10.3934/math.2023260