Conditional Boundary Crossing Probabilities, with Applications to Change-Point Problems
James, Barry ; James, Kang Ling ; Siegmund, David
Ann. Probab., Tome 16 (1988) no. 4, p. 825-839 / Harvested from Project Euclid
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For normal random walks $S_1, S_2,\ldots$, formed from independent identically distributed random variables $X_1, X_2,\ldots$, we determine the asymptotic behavior under regularity conditions of $P(S_n > mg(n/m) \text{for some} n < m\mid S_m = m\xi_0, U_m = m\lambda_0), \quad\xi_0 < g(1),$ where $U_m = X^2_1 + \cdots + X^2_m$. The result is applied to a normal change-point problem to approximate null distributions of test statistics and to obtain approximate confidence sets for the change-point.
Publié le : 1988-04-14
Classification:  Boundary crossing probabilities,  change-point,  normal random walk,  60F10,  60J15,  62F03 
@article{1176991789,
     author = {James, Barry and James, Kang Ling and Siegmund, David},
     title = {Conditional Boundary Crossing Probabilities, with Applications to Change-Point Problems},
     journal = {Ann. Probab.},
     volume = {16},
     number = {4},
     year = {1988},
     pages = { 825-839},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991789}
}

James, Barry; James, Kang Ling; Siegmund, David. Conditional Boundary Crossing Probabilities, with Applications to Change-Point Problems. Ann. Probab., Tome 16 (1988) no. 4, pp.  825-839. http://gdmltest.u-ga.fr/item/1176991789/