Keywords: parametrix, bounded drifts.
@article{TVP_2016_61_3_a7,
author = {A. Kozhina},
title = {Stability of densities for perturbed degenerate diffusions},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {570--579},
year = {2016},
volume = {61},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a7/}
}
A. Kozhina. Stability of densities for perturbed degenerate diffusions. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 3, pp. 570-579. http://geodesic.mathdoc.fr/item/TVP_2016_61_3_a7/
[1] Kolmogorov A. N., Izbrannye trudy. Teoriya veroyatnostei i matematicheskaya statistika, v. 2, Nauka, M., 1986, 581 pp.
[2] Delarue F., Menozzi S., “Density estimates for a random noise propagating through a chain of differential equations”, J. Funct. Anal., 259:6 (2010), 1577–1630 | DOI | MR | Zbl
[3] Dynkin E. B., Markovskie protsessy, GIFML, M., 1963, 861 pp.
[4] Di Francesco M., Pascucci A., “On a class of degenerate parabolic equations of Kolmogorov type”, Appl. Math. Res. Express, 2005, no. 3, 116 | Zbl
[5] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968, 428 pp.
[6] Hérau F., Nier F., “Isotropic hypoelliptic and trend to equilibrium for the Fokker–Planck equation with a high-degree potential”, Arch. Ration. Mech. Anal., 171:2 (2004), 151–218 | DOI | MR | Zbl
[7] Hörmander L., “Hypoelliptic second order differential operators”, Acta. Math., 119 (1967), 147–171 | DOI | MR
[8] Hobson D. G., Rogers L. C. G., “Complete models with stochastic volatility”, Math. Finance, 8:1 (1998), 27–48 | DOI | MR | Zbl
[9] Ilin A. M., Kalashnikov A. S., Oleinik O. A., “Lineinye uravneniya vtorogo poryadka parabolicheskogo tipa”, Uspekhi matem. nauk, 17:3(105) (1962), 3–146
[10] Konakov V., Kozhina A., Menozzi S., {S}tability of densities for perturbed diffusions and {M}arkov chains, 2015, arXiv: 1506.08758v2
[11] Konakov V., Mammen E., “Local limit theorems for transition densities of Markov chains converging to diffusions”, Probab. Theory Relat. Fields, 117:4 (2000), 551–587 | DOI | MR | Zbl
[12] Konakov V., Mammen E., “Edgeworth type expansions for Euler schemes for stochastic differential equations”, Monte Carlo Methods Appl., 8:3 (2002), 271–285 | DOI | MR | Zbl
[13] Konakov V., Menozzi S., Molchanov S., “Explicit parametrix and local limit theorems for some degenerate diffusion processes”, Ann. Inst. Henri Poincaré, Probab. Stat., 46:4 (2010), 908–923 | DOI | MR | Zbl
[14] Kolmogorov A. N., “Sluchainye dvizheniya (k teorii brounovskogo dvizheniya)”, Izbrannye trudy, v. 2, Nauka, M., 2005, 176–177
[15] Krylov N. V., Lektsii po ellipticheskim i parabolicheskim uravneniyam v prostranstve Gëldera, Nauchnaya kniga, Novosibirsk, 1998, 176 pp.
[16] Menozzi S., Lemaire V., “On some non asymptotic bounds for the Euler scheme”, Electron. J. Probab., 15 (2010), 1645–1681 | DOI | MR | Zbl
[17] Menozzi S., “Parametrix techniques and martingale problems for some degenerate Kolmogorov equations”, Electron. Comm. Probab., 17 (2011), 234–250 | DOI | MR
[18] McKean H. P., Singer I. M., “Curvature and the eigenvalues of the Laplacian”, J. Differ. Geom., 1:1 (1967), 43–69 | MR | Zbl
[19] Mattingly J., Stuart A., Higham D., “Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise”, Stoch. Proc. Appl., 101:2 (2002), 185–232 | DOI | MR | Zbl
[20] Norris J. R., “Simplified {M}alliavin calculus”, Probabilités XX, Proc. Sémin, Strasbourg 1984185, Lecture Notes Math., 1204, 1986, 101–130 | DOI | MR | Zbl
[21] Stroock D. W., Varadhan S. R. S., Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979, 388 pp. | MR | Zbl
[22] Talay D., “Stochastic Hamiltonian systems: Exponential convergence to the invariant measure, and discretization by the implicit Euler scheme”, Markov Process. Relat. Fields, 8:2 (2002), 163–198 | MR | Zbl