scholarly journals Nonparametric density estimation in compound Poisson processes using convolution power estimators

Metrika ◽  
2013 ◽  
Vol 77 (1) ◽  
pp. 163-183 ◽  
Author(s):  
Fabienne Comte ◽  
Céline Duval ◽  
Valentine Genon-Catalot
Keyword(s):  
Density Estimation ◽  
Nonparametric Density Estimation ◽  
Poisson Processes ◽  
Compound Poisson ◽  
Compound Poisson Processes ◽  
Convolution Power

Stochastic barriers for the Wiener process

1983 ◽  
Vol 20 (2) ◽  
pp. 338-348 ◽  
Author(s):  
C. Park ◽  
J. A. Beekman
Keyword(s):  
Stochastic Process ◽  
Wiener Process ◽  
Poisson Processes ◽  
Standard Wiener Process ◽  
Compound Poisson ◽  
Compound Poisson Processes ◽  
Deterministic Function

Let {W(t), 0 ≦ t < ∞} be the standard Wiener process. The probabilities of the type P[sup0≦t ≦ TW(t) − f(t) ≧ 0] have been extensively studied when f(t) is a deterministic function. This paper discusses the probabilities of the type P{sup0≦t ≦ TW(t) − [f(t) + X(t)] ≧ 0} when X(t) is a stochastic process. By taking compound Poisson processes as X(t), the paper gives procedures for finding such probabilities.

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