| Title:
|
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients (English) |
| Author:
|
Barbu, Dorel |
| Author:
|
Bocşan, Gheorghe |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
87-95 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
mild solution |
| Keyword:
|
Picard approximations |
| MSC:
|
34F05 |
| MSC:
|
34G20 |
| MSC:
|
35R60 |
| MSC:
|
60H15 |
| idZBL:
|
Zbl 1001.60068 |
| idMR:
|
MR1885459 |
| . |
| Date available:
|
2009-09-24T10:49:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127704 |
| . |
| Reference:
|
[1] R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii: Measures of Noncompactness and Condensing Operators.Birkhauser-Verlag, Basel-Boston-Berlin, 1992. MR 1153247 |
| Reference:
|
[2] V. Bally, I. Gyöngy and E. Pardoux: White noise driven parabolic SPDEs with measurable drift.J. Funct. Anal. 120 (1994), 484–510. MR 1266318, 10.1006/jfan.1994.1040 |
| Reference:
|
[3] D. Barbu: Local and global existence for mild solutions of stochastic differential equations.Portugal. Math. 55 (1998), 411–424. Zbl 0931.60053, MR 1672110 |
| Reference:
|
[4] G. Da Prato and J. Zabczyk: A note on stochastic convolution.Stochastic Anal. Appl. 10 (1992), 143–153. MR 1154532, 10.1080/07362999208809260 |
| Reference:
|
[5] G. Da Prato and J. Zabczyk: Stochastic Equations in Infinite Dimensions.Cambridge Univ. Press, Cambridge, 1992. MR 1207136 |
| Reference:
|
[6] G. Da Prato and J. Zabczyk: Ergodicity for Infinite Dimensional Systems.Cambridge Univ. Press, Cambridge, 1996. MR 1417491 |
| Reference:
|
[7] M. Eddabhi and M. Erraoui: On quasi-linear parabolic SPDEs with non-Lipschitz coefficients.Random Oper. and Stochastic Equations 6 (1998), 105–126. MR 1609543 |
| Reference:
|
[8] A. Ichikawa: Stability of semilinear stochastic evolution equation.J. Math. Anal. Appl. 90 (1982), 12–44. MR 0680861, 10.1016/0022-247X(82)90041-5 |
| Reference:
|
[9] R. Manthey: Convergence of successive approximation for parabolic partial differential equations with additive white noise.Serdica 16 (1990), 194–200. Zbl 0723.65149, MR 1089857 |
| Reference:
|
[10] R. Manthey and T. Zausinger: Stochastic evolution equations in $L_{\rho }^{2\nu }$.Stochastics Stochastics Rep. 66 (1999), 37–85. MR 1687799, 10.1080/17442509908834186 |
| Reference:
|
[11] A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations.Springer Verlag, New York, 1983. Zbl 0516.47023, MR 0710486 |
| Reference:
|
[12] J. Seidler: Da Prato-Zabczyk’s maximal inequality revisited I.Math. Bohem. 118 (1993), 67–106. Zbl 0785.35115, MR 1213834 |
| Reference:
|
[13] T. Taniguchi: On the estimate of solutions of perturbed linear differential equations.J. Math. Anal. Appl. 153 (1990), 288–300. Zbl 0727.34040, MR 1080132, 10.1016/0022-247X(90)90279-O |
| Reference:
|
[14] T. Taniguchi: Successive Approximations to Solutions of Stochastic Differential Equations.J. Differential Equations 96 (1992), 152–169. Zbl 0744.34052, MR 1153313, 10.1016/0022-0396(92)90148-G |
| Reference:
|
[15] L. Tubaro: An estimate of Burkholder type for stochastic processes defined by the stochastic integral.Stochastic Anal. Appl. 2 (1984), 187–192. Zbl 0539.60056, MR 0746435, 10.1080/07362998408809032 |
| Reference:
|
[16] T. Yamada: On the successive approximation of solutions of stochastic differential equations.J. Math. Sci. Univ. Kyoto 21 (1981), 501–515. Zbl 0484.60053, MR 0629781, 10.1215/kjm/1250521975 |
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