Geodesic
Properties of the intrinsically stationary stochastic processes
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2017), pp. 28-33.

Voir la notice de l'article provenant de la source Math-Net.Ru

Intrinsically stationary random processes with continuous time are investigated. Their connections with second-order stationary processes and processes with the second-order stationary increments are studied. The properties of semivariogram of the stationary random processes are investigated. Necessary and sufficient conditions for continuity, differentiability and integrability in the mean square sense of the intrinsically stationary stochastic processes in terms of their semivariogram are found. It is shown that the derivative in the mean square sense of the intrinsically stationary random process, for which the second-order moment is exists, is a second-order stationary random process.
Keywords: stochastic process; intrinsic stationarity; variogram; stochastic analysis. 
@article{BGUMI_2017_1_a4,
     author = {T. V. Tsekhavaya},
     title = {Properties of the intrinsically stationary stochastic processes},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {28--33},
     publisher = {mathdoc},
     volume = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a4/}
}
TY  - JOUR
AU  - T. V. Tsekhavaya
TI  - Properties of the intrinsically stationary stochastic processes
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2017
SP  - 28
EP  - 33
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a4/
LA  - ru
ID  - BGUMI_2017_1_a4
ER  - 
%0 Journal Article
%A T. V. Tsekhavaya
%T Properties of the intrinsically stationary stochastic processes
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2017
%P 28-33
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a4/
%G ru
%F BGUMI_2017_1_a4
T. V. Tsekhavaya. Properties of the intrinsically stationary stochastic processes. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2017), pp. 28-33. http://geodesic.mathdoc.fr/item/BGUMI_2017_1_a4/

[1] A. V. Bulinskii, A. N. Shiryaev, “Teoriya sluchainykh protsessov”, 2005

[2] A. M. Yaglom, “Korrelyatsionnaya teoriya protsessov so sluchainymi statsionarnymi n-mi prirascheniyami”, Matem. sb., 37(79) (1955), 141–196

[3] A. N. Kolmogorov, “Krivye v gilbertovom prostranstve, invariantnye po otnosheniyu k odnoparametricheskoi gruppe dvizhenii”, Dokl. Akad. nauk SSSR, 26(1) (1940), 6–9

[4] N. Cressie, “Statistics for Spatial Data”, New York, 1991

[5] G. Matheron, “Principles of Geostatistics”, Econ. Geol, 58 (1963), 1246–1266

[6] A. N. Kolmogorov, “Lokalnaya struktura turbulentnosti v neszhimaemoi vyazkoi zhidkosti pri ochen bolshikh chislakh Reinoldsa”, Dokl. Akad. nauk SSSR, 30(4) (1941), 299–303

[7] T. V. Tsekhovaya, “Svoistva variogrammy vnutrenne statsionarnykh sluchainykh protsessov”, Teoriya veroyatnostei, matematicheskaya statistika i ikh prilozheniya: materialy Mezhdunar. nauch. konf., 2004, 181–186, Minsk

[8] T. V. Tsekhovaya, “Pervye dva momenta otsenki variogrammy gaussovskogo sluchainogo protsessa”, Differentsialnye uravneniya i sistemy kompyuternoi algebry: materialy Mezhdunar. matem. konf., 2005, 78–82, Brest

[9] M. Loev, “Teoriya veroyatnostei”, 1962

[10] A. D. Venttsel, “Kurs teorii sluchainykh protsessov”, 1975