Limit theorems for jump shock models

1989 ◽  
Vol 26 (4) ◽  
pp. 793-806 ◽  
Author(s):  
Keigo Yamada
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Limit Theorems ◽  
Stable Process ◽  
Deterministic Process ◽  
Shock Process ◽  
Shock Models

We consider an additive shock process where shocks occur according to a Poisson point process and they are accumulated in an appropriate way to the damage. It is shown that suitably normalized shock processes converge weakly to a process which is represented as a sum of a stable process and a deterministic process.

Limit theorems for jump shock models

1989 ◽  
Vol 26 (04) ◽  
pp. 793-806
Author(s):  
Keigo Yamada
Keyword(s):  
Point Process ◽  
Poisson Point Process ◽  
Limit Theorems ◽  
Stable Process ◽  
Deterministic Process ◽  
Shock Process ◽  
Shock Models

We consider an additive shock process where shocks occur according to a Poisson point process and they are accumulated in an appropriate way to the damage. It is shown that suitably normalized shock processes converge weakly to a process which is represented as a sum of a stable process and a deterministic process.

Some Functional Stable Limit Theorems

1973 ◽  
Vol 16 (2) ◽  
pp. 173-177 ◽  
Author(s):  
D. R. Beuerman
Keyword(s):  
Weak Convergence ◽  
Limit Theorems ◽  
Stable Process ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Stable Limit ◽  
Stable Law ◽  
Partial Sum Process ◽  
Image Position

Let Xl,X2,X3, … be a sequence of independent and identically distributed (i.i.d.) random variables which belong to the domain of attraction of a stable law of index α≠1. That is,1whereandwhere L(n) is a function of slow variation; also take S0=0, B0=l.In §2, we are concerned with the weak convergence of the partial sum process to a stable process and the question of centering for stable laws and drift for stable processes.

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