scholarly journals Bernstein–von Mises theorems for statistical inverse problems II: compound Poisson processes

2019 ◽  
Vol 13 (2) ◽  
pp. 3513-3571 ◽  
Author(s):  
Richard Nickl ◽  
Jakob Söhl
Keyword(s):  
Inverse Problems ◽  
Poisson Processes ◽  
Compound Poisson ◽  
Compound Poisson Processes ◽  
Statistical Inverse Problems ◽  
Von Mises

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.

Sign in / Sign up

Export Citation Format

Share Document