Asymptotic Behavior of Homogeneous Additive Functionals of the Solutions to Inhomogeneous Itô SDEs with Non-regular Dependence on a Parameter

Asymptotic Behavior of Homogeneous Additive Functionals Defined on the Solutions of Itô SDEs with Non-regular Dependence on a Parameter

Bocconi & Springer Series - Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations ◽

10.1007/978-3-030-41291-3_5 ◽

2020 ◽

pp. 129-175

Author(s):

Grigorij Kulinich ◽

Svitlana Kushnirenko ◽

Yuliya Mishura

Keyword(s):

Asymptotic Behavior ◽

Additive Functionals ◽

Dependence On A Parameter

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On a Voronoi aggregative process related to a bivariate Poisson process

Advances in Applied Probability ◽

10.1017/s0001867800027506 ◽

1996 ◽

Vol 28 (04) ◽

pp. 965-981 ◽

Cited By ~ 11

Author(s):

S. G. Foss ◽

S. A. Zuyev

Keyword(s):

Asymptotic Behavior ◽

Lower Bounds ◽

Distribution Functions ◽

Poisson Processes ◽

Upper And Lower Bounds ◽

Additive Functionals ◽

Second Moments ◽

Explicit Formulae ◽

Bivariate Poisson Process ◽

Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

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On a Voronoi aggregative process related to a bivariate Poisson process

Advances in Applied Probability ◽

10.2307/1428159 ◽

1996 ◽

Vol 28 (4) ◽

pp. 965-981 ◽

Cited By ~ 131

Author(s):

S. G. Foss ◽

S. A. Zuyev

Keyword(s):

Asymptotic Behavior ◽

Lower Bounds ◽

Distribution Functions ◽

Poisson Processes ◽

Upper And Lower Bounds ◽

Additive Functionals ◽

Second Moments ◽

Explicit Formulae ◽

Bivariate Poisson Process ◽

Sum Of Distances

We consider two independent homogeneous Poisson processes Π0 and Π1 in the plane with intensities λ0 and λ1, respectively. We study additive functionals of the set of Π0-particles within a typical Voronoi Π1-cell. We find the first and the second moments of these variables as well as upper and lower bounds on their distribution functions, implying an exponential asymptotic behavior of their tails. Explicit formulae are given for the number and the sum of distances from Π0-particles to the nucleus within a typical Voronoi Π1-cell.

Download Full-text