Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior

Table 1

Parameters of the numerical example.

Parameter	Value
𝐽	1,2,…,9
𝜆(𝑥)	[…,3𝑗^2𝑥^2,…]^⊤
𝒜	{0,1,…,𝐽−1}
ℳ	{𝐽−1}
𝒩	{𝐽}
𝑀(𝑡)	∑𝑖∈𝒜𝑀𝑖(𝑡)
𝑁(𝑡)	∑𝑖∈ℳ,𝑗∈𝒩𝑁𝑖𝑗(𝑡)
Θ(𝑖,𝑗)	√exp(𝑖−7.9)+exp(7.9−𝑗)
Θ(𝑖,𝑗)	1exp(𝑖+𝑗−5)+21
𝜃	[^Θ(0,0)Θ(0,1)0⋯00⋱⋱0⋮⋮0Θ(𝑖,𝑖)Θ(𝑖,𝑖+1)00⋱⋱⋱Θ(𝐽,𝐽+1)0⋯0Θ(𝐽,𝐽)]
𝜃̂	[Θ^(0,0)Θ(0,1)0⋯00⋱⋱0⋮⋮0Θ(𝑖,𝑖)Θ(𝑖,𝑖+1)00⋱⋱⋱Θ(𝐽,𝐽+1)0⋯0Θ(𝐽,𝐽)]
𝜓𝑑	10
𝜓𝑚	1000
𝑇	1000