Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients

Dorel Barbu; Gheorghe Bocşan

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 1, page 87-95
  • ISSN: 0011-4642

Abstract

top
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.

How to cite

top

Barbu, Dorel, and Bocşan, Gheorghe. "Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients." Czechoslovak Mathematical Journal 52.1 (2002): 87-95. <http://eudml.org/doc/30687>.

@article{Barbu2002,
abstract = {In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.},
author = {Barbu, Dorel, Bocşan, Gheorghe},
journal = {Czechoslovak Mathematical Journal},
keywords = {mild solution; Picard approximations; mild solution; Picard approximations},
language = {eng},
number = {1},
pages = {87-95},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients},
url = {http://eudml.org/doc/30687},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Barbu, Dorel
AU - Bocşan, Gheorghe
TI - Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 87
EP - 95
AB - In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
LA - eng
KW - mild solution; Picard approximations; mild solution; Picard approximations
UR - http://eudml.org/doc/30687
ER -

References

top
  1. Measures of Noncompactness and Condensing Operators, Birkhauser-Verlag, Basel-Boston-Berlin, 1992. (1992) MR1153247
  2. 10.1006/jfan.1994.1040, J.  Funct. Anal. 120 (1994), 484–510. (1994) MR1266318DOI10.1006/jfan.1994.1040
  3. Local and global existence for mild solutions of stochastic differential equations, Portugal. Math. 55 (1998), 411–424. (1998) Zbl0931.60053MR1672110
  4. 10.1080/07362999208809260, Stochastic Anal. Appl. 10 (1992), 143–153. (1992) MR1154532DOI10.1080/07362999208809260
  5. Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, Cambridge, 1992. (1992) MR1207136
  6. Ergodicity for Infinite Dimensional Systems, Cambridge Univ. Press, Cambridge, 1996. (1996) MR1417491
  7. On quasi-linear parabolic SPDEs with non-Lipschitz coefficients, Random Oper. and Stochastic Equations 6 (1998), 105–126. (1998) MR1609543
  8. 10.1016/0022-247X(82)90041-5, J.  Math. Anal. Appl. 90 (1982), 12–44. (1982) MR0680861DOI10.1016/0022-247X(82)90041-5
  9. Convergence of successive approximation for parabolic partial differential equations with additive white noise, Serdica 16 (1990), 194–200. (1990) Zbl0723.65149MR1089857
  10. 10.1080/17442509908834186, Stochastics Stochastics Rep. 66 (1999), 37–85. (1999) MR1687799DOI10.1080/17442509908834186
  11. Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983. (1983) Zbl0516.47023MR0710486
  12. Da Prato-Zabczyk’s maximal inequality revisited I, Math. Bohem. 118 (1993), 67–106. (1993) Zbl0785.35115MR1213834
  13. 10.1016/0022-247X(90)90279-O, J.  Math. Anal. Appl. 153 (1990), 288–300. (1990) Zbl0727.34040MR1080132DOI10.1016/0022-247X(90)90279-O
  14. 10.1016/0022-0396(92)90148-G, J.  Differential Equations 96 (1992), 152–169. (1992) Zbl0744.34052MR1153313DOI10.1016/0022-0396(92)90148-G
  15. 10.1080/07362998408809032, Stochastic Anal. Appl. 2 (1984), 187–192. (1984) Zbl0539.60056MR0746435DOI10.1080/07362998408809032
  16. 10.1215/kjm/1250521975, J.  Math. Sci. Univ. Kyoto 21 (1981), 501–515. (1981) Zbl0484.60053MR0629781DOI10.1215/kjm/1250521975

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.