多类型连续状态分支过程的消灭时间

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2021-09-07 DOI:10.1214/22-aihp1279
L. Chaumont, M. Marolleau
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引用次数: 3

摘要

多类型连续状态分支过程(MCSBP) ${\rm Z}=({\rm Z}_{t})_{t\geq 0}$是一个值在$[0,\infty)^{d}$满足分支性质的马尔可夫过程。它的分布以分支机制为特征,即$\mathbb{R}^d$值谱正的l逍遥过程的$d$拉普拉斯指数的数据,每一个都有$d-1$递增分量。我们给出了MCSBP在无穷远处趋于0的概率表达式。然后我们证明,当且仅当分支机制的某些条件成立时,这种灭绝在有限时间内成立。这种情况延伸了格蕾的病情,众所周知的$d=1$。我们的论点涉及到最近在\cite{cma1}中得到的谱正加性lsamvy场的涨落理论的要素和在\cite{cpgub}中证明的高维Lamperti表示的推广。
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Extinction times of multitype continuous-state branching processes
A multitype continuous-state branching process (MCSBP) ${\rm Z}=({\rm Z}_{t})_{t\geq 0}$, is a Markov process with values in $[0,\infty)^{d}$ that satisfies the branching property. Its distribution is characterised by its branching mechanism, that is the data of $d$ Laplace exponents of $\mathbb{R}^d$-valued spectrally positive L\'evy processes, each one having $d-1$ increasing components. We give an expression of the probability for a MCSBP to tend to 0 at infinity in term of its branching mechanism. Then we prove that this extinction holds at a finite time if and only if some condition bearing on the branching mechanism holds. This condition extends Grey's condition that is well known for $d=1$. Our arguments bear on elements of fluctuation theory for spectrally positive additive L\'evy fields recently obtained in \cite{cma1} and an extension of the Lamperti representation in higher dimension proved in \cite{cpgub}.
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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