A growth estimate for continuous random fields

Ralf Manthey; Katrin Mittmann

Mathematica Bohemica (1996)

  • Volume: 121, Issue: 4, page 397-413
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Manthey, Ralf, and Mittmann, Katrin. "A growth estimate for continuous random fields." Mathematica Bohemica 121.4 (1996): 397-413. <http://eudml.org/doc/247975>.

@article{Manthey1996,
abstract = {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.},
author = {Manthey, Ralf, Mittmann, Katrin},
journal = {Mathematica Bohemica},
keywords = {asymptotic behaviour of paths; Wiener field; stochastic diffusion equation; asymptotic behaviour of paths; Wiener field; stochastic diffusion equation},
language = {eng},
number = {4},
pages = {397-413},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A growth estimate for continuous random fields},
url = {http://eudml.org/doc/247975},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Manthey, Ralf
AU - Mittmann, Katrin
TI - A growth estimate for continuous random fields
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 4
SP - 397
EP - 413
AB - 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.
LA - eng
KW - asymptotic behaviour of paths; Wiener field; stochastic diffusion equation; asymptotic behaviour of paths; Wiener field; stochastic diffusion equation
UR - http://eudml.org/doc/247975
ER -

References

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  1. G. DaPrato J. Zabczyk, Stochastic equations in infinite dimensions, Cambridge University Press, 1992. (1992) MR1207136
  2. A. Friedman, Partial differential equations of parabolic type, Pгentice Hall, Englewood Cliffs, N.Y., 1964. (1964) Zbl0144.34903MR0181836
  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. (1972) MR0410880
  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.) (1962) MR0138888
  5. R. S. Liptser A. N. Shiryaev, Martingale theory, Nauka, Moscow, 1986. (In Russian.) (1986) MR0886678
  6. R. Manthey, 10.1002/mana.19881360114, Math. Nachr. 136 (1988), 209-228. (1988) Zbl0658.60089MR0952473DOI10.1002/mana.19881360114
  7. R. Redlinger, Existenzsätze für semilineare parabolische Systeme mit Funktionalen, Dissertation Universität Karlsruhe, 1982. (1982) Zbl0535.35038
  8. R. Redlinger, 10.1016/0362-546X(84)90011-7, Nonlinear Analysis 8(6) (1984), 667-682. (1984) Zbl0543.35052MR0746724DOI10.1016/0362-546X(84)90011-7
  9. J. B. Walsh, 10.1007/BFb0074920, Lect. Notes in Math. vol. 1180, Spгinger, 1986, 265-439. (1986) Zbl0608.60060MR0876085DOI10.1007/BFb0074920

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