On stochastic differential equations with locally unbounded drift

István Gyöngy; Teresa Martínez

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 4, page 763-783
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Gyöngy, István, and Martínez, Teresa. "On stochastic differential equations with locally unbounded drift." Czechoslovak Mathematical Journal 51.4 (2001): 763-783. <http://eudml.org/doc/30670>.

@article{Gyöngy2001,
abstract = {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.},
author = {Gyöngy, István, Martínez, Teresa},
journal = {Czechoslovak Mathematical Journal},
keywords = {stochastic differential equations; Krylov’s estimate; stochastic differential equations; Krylov's estimate},
language = {eng},
number = {4},
pages = {763-783},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On stochastic differential equations with locally unbounded drift},
url = {http://eudml.org/doc/30670},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Gyöngy, István
AU - Martínez, Teresa
TI - On stochastic differential equations with locally unbounded drift
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 763
EP - 783
AB - 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.
LA - eng
KW - stochastic differential equations; Krylov’s estimate; stochastic differential equations; Krylov's estimate
UR - http://eudml.org/doc/30670
ER -

References

top
  1. Diffusions with singular drift related to wave functions, Probab. Theory Related Fields 96 (1996), 107–121. (1996) MR1222367
  2. Uniqueness of solutions of stochastic differential equations, 2001, preprint. Zbl1139.60028MR2377011
  3. 10.1002/mana.19841190108, Math. Nachr. 119 (1984), 97–115. (1984) MR0774179DOI10.1002/mana.19841190108
  4. 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. (1985) MR0798317
  5. On stochastic differential equations with irregular coefficients, Technical Report Series of the Laboratory for Research in Statistics and Probability 91 (1986). (1986) 
  6. 10.1080/17442509208833782, Stochastics Stochastics Rep. 40 (1992), 77–115. (1992) MR1275128DOI10.1080/17442509208833782
  7. Existence of strong solutions for Itô’s stochastic equations via approximations, Probab. Theory Related Fields 105 (1996), 143–158. (1996) MR1392450
  8. 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. (1988) MR0960522
  9. On some estimates of the distribution of stochastic integrals, Izv. Akad. Nauk SSSR Ser. Math. 38 (1974), 228–248. (Russian) (1974) MR0345206
  10. 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) (1986) MR0854972
  11. Controlled Diffusion Processes, Nauka, Moscow, 1977, English transl.: Springer-Verlag, New York-Berlin, 1980. (1977) MR0601776
  12. Linear and Quasilinear Equations of Parabolic Type, Nauka, Moscow, 1967, English transl.: American Mathematical Society, Providence, R.I., 1968. (1967) 
  13. Statistics of Random Processes I, Nauka, Moscow, 1974, English transl.: Springer-Verlag, New York-Heidelberg, 1977. (1974) 
  14. Quelques résultats de “mécanique stochastique”, Séminaire de Probabilités XVIII. Lecture Notes in Mathematics Vol.  1059, Springer, Berlin-New York, 1984, pp. 223–244. (1984) MR0770964
  15. Sur la construction des certaines diffusions, Séminaire de Probabilités XX. Lecture Notes in Mathematics Vol.  1204, Springer, Berlin-New York, 1986, pp. 334–337. (1986) MR0942027
  16. 10.1007/BF00340014, Probab. Theory Related Fields 82 (1989), 109-136. (1989) MR0997433DOI10.1007/BF00340014
  17. 10.1007/BF00532640, Z.  Wahrsch. Verw. Gebiete 68 (1985), 247–269. (1985) MR0771466DOI10.1007/BF00532640
  18. Generalized Diffusion Processes, Naukova Dumka, Kiev, 1982, English transl.: American Mathematical Society, Providence, R.I., 1990. (1982) Zbl0727.60089MR1104660
  19. Studies in the Theory of Random Processes, Izdat. Kiev. Univ., Kiev, 1961, English transl.: Addison Wesley Publ. Co., Reading, Mass., 1965. (1961) MR0185620
  20. Multidimensional Diffusion Processes, Springer-Verlag, Berlin, 1979. (1979) MR0532498
  21. 10.1007/BF01192962, Probab. Theory Related Fields 97 (1993), 515–542. (1993) Zbl0794.60055MR1246978DOI10.1007/BF01192962
  22. On the strong solutions of stochastic differential equations, Theory Probab. Appl. 24 (1979), 354–366. (1979) Zbl0418.60061MR0532447
  23. Parabolic equations and stochastic Itô differential equations with discontinuous coefficients in time, Mat. Zametki 31 (1982), 549–557. (Russian) (1982) MR0657716
  24. 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) (1974) MR0336813

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.