| Title:
|
A growth estimate for continuous random fields (English) |
| Author:
|
Manthey, Ralf |
| Author:
|
Mittmann, Katrin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
121 |
| Issue:
|
4 |
| Year:
|
1996 |
| Pages:
|
397-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a polynomial growth estimate for random fields satisfying the Kolmogorov continuity test. As an application we are able to estimate the growth of the solution to the Cauchy problem for a stochastic diffusion equation. (English) |
| Keyword:
|
asymptotic behaviour of paths |
| Keyword:
|
Wiener field |
| Keyword:
|
stochastic diffusion equation |
| MSC:
|
60G15 |
| MSC:
|
60G17 |
| MSC:
|
60G60 |
| MSC:
|
60H15 |
| idZBL:
|
Zbl 0879.60039 |
| idMR:
|
MR1428142 |
| DOI:
|
10.21136/MB.1996.126035 |
| . |
| Date available:
|
2009-09-24T21:21:27Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126035 |
| . |
| Reference:
|
[1] G. DaPrato J. Zabczyk: Stochastic equations in infinite dimensions.Cambridge University Press, 1992. MR 1207136 |
| Reference:
|
[2] A. Friedman: Partial differential equations of parabolic type.Pгentice Hall, Englewood Cliffs, N.Y., 1964. Zbl 0144.34903, MR 0181836 |
| Reference:
|
[3] A. Garsia: Continuity properties of Gaussian pгocesses with multidimensional time parameter.Proc. бth Berkeley Symp. Math. Statistics and Probability. Univ. California Press, Berkeley and L. A., 1972, pp. 369-374. MR 0410880 |
| Reference:
|
[4] A. M. Iljin A. C. Kalashnikov O. A. Olejnik: Second order linear equations of parabolic type.Uspekhi Mat. Nauk 17(3) (1962), 3-146. (In Russian.) MR 0138888 |
| Reference:
|
[5] R. S. Liptser A. N. Shiryaev: Martingale theory.Nauka, Moscow, 1986. (In Russian.) MR 0886678 |
| Reference:
|
[6] R. Manthey: On the Cauchy problem for reaction-diffusion equations with white noise.Math. Nachr. 136 (1988), 209-228. Zbl 0658.60089, MR 0952473, 10.1002/mana.19881360114 |
| Reference:
|
[7] R. Redlinger: Existenzsätze für semilineare parabolische Systeme mit Funktionalen.Dissertation Universität Karlsruhe, 1982. Zbl 0535.35038 |
| Reference:
|
[8] R. Redlinger: Existence theorems for semilinear parabolic systems with functionals.Nonlinear Analysis 8(6) (1984), 667-682. Zbl 0543.35052, MR 0746724, 10.1016/0362-546X(84)90011-7 |
| Reference:
|
[9] J. B. Walsh: An introduction to stochastic partial differential equations.Lect. Notes in Math. vol. 1180, Spгinger, 1986, 265-439. Zbl 0608.60060, MR 0876085, 10.1007/BFb0074920 |
| . |
