RANDOM SWITCHING BETWEEN VECTOR FIELDS HAVING A COMMON ZERO
RANDOM SWITCHING BETWEEN VECTOR FIELDS HAVING A COMMON ZERO
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DOI：
10.1214/18-aap1418
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发表时间：
2019-02-01
影响因子：
1.8
通讯作者：
Strickler, Edouard
中科院分区：
文献类型：
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作者：
Benaim, Michel;Strickler, Edouard
设E是一个有限集，{F-i}（i是E的一个元素）是R-d上的一个向量场族，它离开紧集M是正不变的，且有一个公共零点p是M的一个元素。我们考虑MxE上的分段确定性马尔可夫过程（X，I），定义为（X）在点（t）=F（I）t（X-t）上，其中I是由X控制的跳跃过程：PR（It+s = j垂直条（X-u，I-u））当λ（+）< 0且（X，当λ（-）> 0时，I）在分布中以指数速率收敛于由M \ {p} x E支持的（唯一）不变测度。讨论了在波动环境中某些传染病模型的应用，并举例说明了我们的结果。
Let E be a finite set, {F-i}(i is an element of E) a family of vector fields on R-d leaving positively invariant a compact set M and having a common zero p is an element of M. We consider a piecewise deterministic Markov process (X, I) on M x E defined by (X)over dot(t)=F(I)t(X-t) where I is a jump process controlled by X: Pr(It+s = j vertical bar(X-u ,I-u)(u p exponentially fast when Lambda(+) < 0 and (X, I) converges in distribution at an exponential rate toward a (unique) invariant measure supported by M \ {p} x E when Lambda(-) > 0. Some applications to certain epidemic models in a fluctuating environment are discussed and illustrate our results.