Soit une fonction non négative singulière seulement pour : , . On étudie le comportement du processus de Wiener dans les voisinages à droite et à gauche des traversées d’un niveau, et on donne des conditions nécessaires et suffisantes pour que les intégrales de soient finies ou infinies.
Let be a nonnegative function with its only singularity at , e.g. , . We study the behavior of the Wiener process in left and right hand neighborhoods of level crossings by finding necessary and sufficient conditions on for the integrals of to be finite or infinite.
@article{AIF_1974__24_2_189_0, author = {Shepp, Lawrence A. and Klauder, John R. and Ezawa, Hiroshi}, title = {On the divergence of certain integrals of the {Wiener} process}, journal = {Annales de l'Institut Fourier}, pages = {189--193}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {24}, number = {2}, year = {1974}, doi = {10.5802/aif.512}, mrnumber = {53 #6772}, zbl = {0275.60088}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.512/} }
TY - JOUR AU - Shepp, Lawrence A. AU - Klauder, John R. AU - Ezawa, Hiroshi TI - On the divergence of certain integrals of the Wiener process JO - Annales de l'Institut Fourier PY - 1974 SP - 189 EP - 193 VL - 24 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.512/ DO - 10.5802/aif.512 LA - en ID - AIF_1974__24_2_189_0 ER -
%0 Journal Article %A Shepp, Lawrence A. %A Klauder, John R. %A Ezawa, Hiroshi %T On the divergence of certain integrals of the Wiener process %J Annales de l'Institut Fourier %D 1974 %P 189-193 %V 24 %N 2 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.512/ %R 10.5802/aif.512 %G en %F AIF_1974__24_2_189_0
Shepp, Lawrence A.; Klauder, John R.; Ezawa, Hiroshi. On the divergence of certain integrals of the Wiener process. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 189-193. doi : 10.5802/aif.512. http://archive.numdam.org/articles/10.5802/aif.512/
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