Previous |  Up |  Next

Article

Title: On stochastic differential equations with locally unbounded drift (English)
Author: Gyöngy, István
Author: Martínez, Teresa
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 51
Issue: 4
Year: 2001
Pages: 763-783
Summary lang: English
.
Category: math
.
Summary: We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift. (English)
Keyword: stochastic differential equations
Keyword: Krylov’s estimate
MSC: 60H10
MSC: 60H40
idZBL: Zbl 1001.60060
idMR: MR1864041
.
Date available: 2009-09-24T10:47:06Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/127685
.
Reference: [1] R. Aebi: Diffusions with singular drift related to wave functions.Probab. Theory Related Fields 96 (1996), 107–121. MR 1222367
Reference: [2] A. M. Davie: Uniqueness of solutions of stochastic differential equations.2001, preprint. Zbl 1139.60028, MR 2377011
Reference: [3] H. J.  Engelbert and W. Schmidt: On exponential local martingales connected with diffusion processes.Math. Nachr. 119 (1984), 97–115. MR 0774179, 10.1002/mana.19841190108
Reference: [4] H. J.  Engelbert and W. Schmidt: On one-dimensional stochastic differential equations with generalized drift. Stochastic Differential Systems (Marseille-Luminy, 1984).Lecture Notes in Control and Information Sci. Vol. 69, Springer, Berlin-New York, 1985, pp. 143–155. MR 0798317
Reference: [5] I. Gyöngy: On stochastic differential equations with irregular coefficients.Technical Report Series of the Laboratory for Research in Statistics and Probability 91 (1986).
Reference: [6] I.  Gyöngy and N. V. Krylov: Stochastic partial differential equations with unbounded coefficients and applications III.Stochastics Stochastics Rep. 40 (1992), 77–115. MR 1275128, 10.1080/17442509208833782
Reference: [7] I. Gyöngy and N. V. Krylov: Existence of strong solutions for Itô’s stochastic equations via approximations.Probab. Theory Related Fields 105 (1996), 143–158. MR 1392450
Reference: [8] H.  Kaneko and S. Nakao: A note on approximation for stochastic differential equations. Séminaire de Probabilités XXII.Lecture Notes in Mathematics Vol. 1321, Springer, Berlin-New York, 1988, pp. 155–162. MR 0960522
Reference: [9] N. V. Krylov: On some estimates of the distribution of stochastic integrals.Izv. Akad. Nauk SSSR Ser. Math. 38 (1974), 228–248. (Russian) MR 0345206
Reference: [10] N. V. Krylov: Estimates of the maximum of the solution of a parabolic equation and estimates of the distribution of a semimartingale.Mat. Sb. (N.S.) 130 (172) (1986), 207–221. (Russian) MR 0854972
Reference: [11] N. V. Krylov: Controlled Diffusion Processes.Nauka, Moscow, 1977, English transl.: Springer-Verlag, New York-Berlin, 1980. MR 0601776
Reference: [12] O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Ural’ceva: Linear and Quasilinear Equations of Parabolic Type.Nauka, Moscow, 1967, English transl.: American Mathematical Society, Providence, R.I., 1968.
Reference: [13] R. S. Liptser and A. N. Shiryaev: Statistics of Random Processes I.Nauka, Moscow, 1974, English transl.: Springer-Verlag, New York-Heidelberg, 1977.
Reference: [14] P. A. Meyer and W. A.  Zheng: Quelques résultats de “mécanique stochastique”.Séminaire de Probabilités XVIII. Lecture Notes in Mathematics Vol.  1059, Springer, Berlin-New York, 1984, pp. 223–244. MR 0770964
Reference: [15] P. A. Meyer and W. A. Zheng: Sur la construction des certaines diffusions.Séminaire de Probabilités XX. Lecture Notes in Mathematics Vol.  1204, Springer, Berlin-New York, 1986, pp. 334–337. MR 0942027
Reference: [16] M.  Nagasawa: Transformations of diffusions and Schrödinger processes.Probab. Theory Related Fields 82 (1989), 109-136. MR 0997433, 10.1007/BF00340014
Reference: [17] M. Nagasawa, H.  Tanaka: Diffusion process in a singular mean-drift-field.Z.  Wahrsch. Verw. Gebiete 68 (1985), 247–269. MR 0771466, 10.1007/BF00532640
Reference: [18] N. I.  Portenko: Generalized Diffusion Processes.Naukova Dumka, Kiev, 1982, English transl.: American Mathematical Society, Providence, R.I., 1990. Zbl 0727.60089, MR 1104660
Reference: [19] A. V. Skorohod: Studies in the Theory of Random Processes.Izdat. Kiev. Univ., Kiev, 1961, English transl.: Addison Wesley Publ. Co., Reading, Mass., 1965. MR 0185620
Reference: [20] D. W.  Stroock, S. R. S. Varadhan: Multidimensional Diffusion Processes.Springer-Verlag, Berlin, 1979. MR 0532498
Reference: [21] W.  Stummer: The Novikov and entropy conditions of multidimensional diffusion processes with singular drift.Probab. Theory Related Fields 97 (1993), 515–542. Zbl 0794.60055, MR 1246978, 10.1007/BF01192962
Reference: [22] A. Ju. Veretennikov: On the strong solutions of stochastic differential equations.Theory Probab. Appl. 24 (1979), 354–366. Zbl 0418.60061, MR 0532447
Reference: [23] A. Yu.  Veretennikov: Parabolic equations and stochastic Itô differential equations with discontinuous coefficients in time.Mat. Zametki 31 (1982), 549–557. (Russian) MR 0657716
Reference: [24] A. K. Zvonkin: A transformation of the phase space of a diffusion process that will remove the drift.Mat. Sb. (N.S.) 93 (135) (1974), 129–149. (Russian) MR 0336813
.

Files

Files Size Format View
CzechMathJ_51-2001-4_8.pdf 450.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo