Let be a stochastically continuous, separable, Gaussian process with . A sufficient condition, in terms of the monotone rearrangement of , is obtained for to have continuous sample paths almost surely. This result is applied to a wide class of random series of functions, in particular, to random Fourier series.
Soit un processus gaussien séparable et stochastiquement continu, satisfaisant à la condition . On obtient une condition suffisante de continuité presque sûre de , mise en termes de ré-arrangement monotone de . On fait l’application de ce résultat aux séries des fonctions aléatoires, en particulier, aux séries aléatoires de Fourier.
@article{AIF_1974__24_2_117_0, author = {Jain, Naresh C. and Marcus, Michael B.}, title = {Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions}, journal = {Annales de l'Institut Fourier}, pages = {117--141}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {24}, number = {2}, year = {1974}, doi = {10.5802/aif.508}, zbl = {0283.60041}, mrnumber = {54 #1356}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.508/} }
TY - JOUR AU - Jain, Naresh C. AU - Marcus, Michael B. TI - Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions JO - Annales de l'Institut Fourier PY - 1974 SP - 117 EP - 141 VL - 24 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.508/ DO - 10.5802/aif.508 LA - en ID - AIF_1974__24_2_117_0 ER -
%0 Journal Article %A Jain, Naresh C. %A Marcus, Michael B. %T Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions %J Annales de l'Institut Fourier %D 1974 %P 117-141 %V 24 %N 2 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.508/ %R 10.5802/aif.508 %G en %F AIF_1974__24_2_117_0
Jain, Naresh C.; Marcus, Michael B. Sufficient conditions for the continuity of stationary gaussian processes and applications to random series of functions. Annales de l'Institut Fourier, Volume 24 (1974) no. 2, pp. 117-141. doi : 10.5802/aif.508. https://aif.centre-mersenne.org/articles/10.5802/aif.508/
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