Geodesic
Invariance Theorems for First Passage Time Random Variables
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 171-176

Voir la notice de l'article provenant de la source Cambridge

DOI

Let X 1X 2,... be i.i.d. r.v. with EX=μ>0, and E(X-μ)2 = σ2<∞.Let S k =X 1+...+X k and v x =max{k:S k ≤x}, x≥0 and v x =0 if X 1>x. Billingsley [1] proved if X1≥0 then converges weakly to the Wiener measure W.Let τx (ω)=inf{k≥1|S k >x}. In §2 we prove that converges weakly to the Wiener measure when the X's may not necessarily be nonnegative. Also we indicate that this result can be extended to the nonidentical case. 
Basu, A. K. Invariance Theorems for First Passage Time Random Variables. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 171-176. doi: 10.4153/CMB-1972-031-9
@article{10_4153_CMB_1972_031_9,
     author = {Basu, A. K.},
     title = {Invariance {Theorems} for {First} {Passage} {Time} {Random} {Variables}},
     journal = {Canadian mathematical bulletin},
     pages = {171--176},
     year = {1972},
     volume = {15},
     number = {2},
     doi = {10.4153/CMB-1972-031-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-031-9/}
}
TY  - JOUR
AU  - Basu, A. K.
TI  - Invariance Theorems for First Passage Time Random Variables
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 171
EP  - 176
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-031-9/
DO  - 10.4153/CMB-1972-031-9
ID  - 10_4153_CMB_1972_031_9
ER  - 
%0 Journal Article
%A Basu, A. K.
%T Invariance Theorems for First Passage Time Random Variables
%J Canadian mathematical bulletin
%D 1972
%P 171-176
%V 15
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-031-9/
%R 10.4153/CMB-1972-031-9
%F 10_4153_CMB_1972_031_9

Cité par Sources :