Maximal inequalities and space-time regularity of stochastic convolutions

Szymon Peszat; Jan Seidler

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 1, page 7-32
  • ISSN: 0862-7959

Abstract

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Space-time regularity of stochastic convolution integrals J = 0 S(-r)Z(r)W(r) driven by a cylindrical Wiener process W in an L 2 -space on a bounded domain is investigated. The semigroup S is supposed to be given by the Green function of a 2 m -th order parabolic boundary value problem, and Z is a multiplication operator. Under fairly general assumptions, J is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well.

How to cite

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Peszat, Szymon, and Seidler, Jan. "Maximal inequalities and space-time regularity of stochastic convolutions." Mathematica Bohemica 123.1 (1998): 7-32. <http://eudml.org/doc/248307>.

@article{Peszat1998,
abstract = {Space-time regularity of stochastic convolution integrals J = 0 S(-r)Z(r)W(r) driven by a cylindrical Wiener process $W$ in an $L^2$-space on a bounded domain is investigated. The semigroup $S$ is supposed to be given by the Green function of a $2m$-th order parabolic boundary value problem, and $Z$ is a multiplication operator. Under fairly general assumptions, $J$ is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well.},
author = {Peszat, Szymon, Seidler, Jan},
journal = {Mathematica Bohemica},
keywords = {stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations; stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations},
language = {eng},
number = {1},
pages = {7-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Maximal inequalities and space-time regularity of stochastic convolutions},
url = {http://eudml.org/doc/248307},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Peszat, Szymon
AU - Seidler, Jan
TI - Maximal inequalities and space-time regularity of stochastic convolutions
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 1
SP - 7
EP - 32
AB - Space-time regularity of stochastic convolution integrals J = 0 S(-r)Z(r)W(r) driven by a cylindrical Wiener process $W$ in an $L^2$-space on a bounded domain is investigated. The semigroup $S$ is supposed to be given by the Green function of a $2m$-th order parabolic boundary value problem, and $Z$ is a multiplication operator. Under fairly general assumptions, $J$ is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well.
LA - eng
KW - stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations; stochastic convolutions; maximal inequalities; regularity of stochastic partial differential equations
UR - http://eudml.org/doc/248307
ER -

References

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