Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2014_95_2_a3, author = {V. P. Demichev}, title = {A {Central} {Limit} {Theorem} for {Integrals} with {Respect} to {Random} {Measures}}, journal = {Matemati\v{c}eskie zametki}, pages = {209--221}, publisher = {mathdoc}, volume = {95}, number = {2}, year = {2014}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a3/} }
V. P. Demichev. A Central Limit Theorem for Integrals with Respect to Random Measures. Matematičeskie zametki, Tome 95 (2014) no. 2, pp. 209-221. http://geodesic.mathdoc.fr/item/MZM_2014_95_2_a3/
[1] S. N. Gurbatov, A. N. Malakhov, A. I. Saichev, Nelineinye sluchainye volny v sredakh bez dispersii, Sovremennye problemy fiziki, 81, Nauka, M., 1990 | MR
[2] W. A. Woyczyński, “Burgers-KPZ Turbulence. Göttingen Lectures”, Lecture Notes in Math., 1700, Springer-Verlag, Berlin, 1998 | DOI | MR | Zbl
[3] S. F. Shandarin, Ya. B. Zeldovich, “The large scale structure of the universe: turbulence, intermittency, structures in a self-gravitating medium”, Rev. Mod. Phys., 61:2 (1989), 185–220 | DOI | MR
[4] A. V. Bulinskii, S. A. Molchanov, “Asimptoticheskaya gaussovost resheniya uravneniya Byurgersa so sluchainymi nachalnymi dannymi”, TVP, 36:2 (1991), 217–235 | MR | Zbl
[5] A. V. Bulinskii, “Some problems of asymptotical analysis of nonlinear diffusion”, Probability Theory and Mathematical Statistics, eds. A. N. Shiryaev et al., World Sci. Publ., Singapore, 1992, 32–46 | MR | Zbl
[6] A. V. Bulinskii, “CLT for the solution of the multidimensional Burgers equation with random data”, Ann. Acad. Sci. Fenn. Ser. A I Math., 17:1 (1992), 11–22 | MR | Zbl
[7] T. Funaki, D. Surgailis, W. A. Woyczynski, “Gibbs-Cox random fields and Burgers turbulence”, Ann. Appl. Probab., 5:2 (1995), 461–492 | DOI | MR | Zbl
[8] N. Leonenko, E. Orsingher, “Limit theorems for solutions of the Burgers equation with Gaussian and non-Gaussian initial conditions”, TVP, 40:2 (1995), 387–403 | MR | Zbl
[9] S. A. Molchanov, D. Surgailis, W. A. Woyczynski, “Hyperbolic asymptotics in Burgers' turbulence and extremal processes”, Comm. Math. Phys., 168:1 (1995), 209–226 | DOI | MR | Zbl
[10] Ya. G. Sinai, “Two results concerning asymptotic behaviour of solutions of the Burgers equation with force”, J. Stat. Phys., 64:1-2 (1991), 1–12 | DOI | MR | Zbl
[11] O. E. Barndorff-Nielsen, N. N. Leonenko, “Burgers' turbulence problem with linear or quadratic external potential”, J. Appl. Probab., 42:2 (2005), 550–565 | DOI | MR | Zbl
[12] N. N. Leonenko, M. D. Ruiz-Medina, “Scaling laws for the multidimensional Burgers equation with quadratic external potential”, J. Stat. Phys., 124:1 (2006), 191–205 | DOI | MR | Zbl
[13] Yu. Yu. Bakhtin, “Funktsionalnaya tsentralnaya predelnaya teorema dlya resheniya mnogomernogo uravneniya Byurgersa s nachalnymi dannymi, zadannymi assotsiirovannoi sluchainoi meroi”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2000, no. 6, 8–15 | MR | Zbl
[14] Yu. Yu. Bakhtin, “Funktsionalnaya tsentralnaya predelnaya teorema dlya preobrazovannykh reshenii mnogomernogo uravneniya Byurgersa so sluchainymi nachalnymi dannymi”, TVP, 46:3 (2001), 427–448 | DOI | MR | Zbl
[15] A. Bulinski, C. Suquet, “Normal approximation for quasi-associated random fields”, Statist. Probab. Lett., 54:2 (2001), 215–226 | DOI | MR | Zbl
[16] S. N. Evans, “Association and random measures”, Probab. Theory Related Fields, 86:1 (1990), 1–19 | DOI | MR | Zbl
[17] A. V. Bulinskii, A. P. Shashkin, Predelnye teoremy dlya assotsiirovannykh sluchainykh polei i rodstvennykh sistem, Fizmatlit, M., 2008
[18] A. V. Bulinskii, E. Shabanovich, “Asimptoticheskoe povedenie nekotorykh funktsionalov ot polozhitelno i otritsatelno zavisimykh sluchainykh polei”, Fundament. i prikl. matem., 4:2 (1998), 479–492 | MR | Zbl
[19] A. P. Shashkin, “Kvaziassotsiirovannost gaussovskoi sistemy sluchainykh vektorov”, UMN, 57:6(348) (2002), 199–200 | DOI | MR | Zbl
[20] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, T. 2, Mir, M., 1984 | MR | Zbl
[21] A. V. Bulinski, E. Spodarev, F. Timmermann, “Central limit theorems for the excursion set volumes of weakly dependent random fields”, Bernoulli, 18:1 (2012), 100–118 | DOI | MR | Zbl
[22] A. Bulinski, “Central limit theorem for random fields and applications”, Advances in Data Analysis, Stat. Ind. Technol., Birkhäuser Boston, Boston, MA, 2010, 141–150 | MR
[23] H. Yu, “A Glivenko–Cantelli lemma and weak convergence for empirical processes of associated sequences”, Probab. Theory Related Fields, 95:3 (1993), 357–370 | DOI | MR | Zbl
[24] J. M. Burgers, The Nonlinear Diffusion Equation. Asymptotic Solutions and Statistical Problems, D. Reidel Publ., Boston, 1974 | Zbl
[25] P. J. Bickel, M. J. Wichura, “Convergence criteria for multiparameter Stochastic processes and some applications”, Ann. Math. Statist., 42:5 (1971), 1656–1670 | DOI | MR | Zbl