A note on maximal inequality for stochastic convolutions

Erika Hausenblas; Jan Seidler

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 4, page 785-790
  • ISSN: 0011-4642

Abstract

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Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution ∫ 0 t S ( t - s ) ψ ( s ) d W ( s ) driven by a Wiener process W in a Hilbert space in the case when the semigroup S ( t ) is of contraction type.

How to cite

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Hausenblas, Erika, and Seidler, Jan. "A note on maximal inequality for stochastic convolutions." Czechoslovak Mathematical Journal 51.4 (2001): 785-790. <http://eudml.org/doc/30671>.

@article{Hausenblas2001,
abstract = {Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution \[ \int ^t\_0 S(t-s)\psi (s)\mathrm \{d\}W(s) \] driven by a Wiener process $W$ in a Hilbert space in the case when the semigroup $S(t)$ is of contraction type.},
author = {Hausenblas, Erika, Seidler, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {infinite-dimensional Wiener process; stochastic convolution; maximal inequality; infinite-dimensional Wiener process; stochastic convolution; maximal inequality},
language = {eng},
number = {4},
pages = {785-790},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on maximal inequality for stochastic convolutions},
url = {http://eudml.org/doc/30671},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Hausenblas, Erika
AU - Seidler, Jan
TI - A note on maximal inequality for stochastic convolutions
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 785
EP - 790
AB - Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution \[ \int ^t_0 S(t-s)\psi (s)\mathrm {d}W(s) \] driven by a Wiener process $W$ in a Hilbert space in the case when the semigroup $S(t)$ is of contraction type.
LA - eng
KW - infinite-dimensional Wiener process; stochastic convolution; maximal inequality; infinite-dimensional Wiener process; stochastic convolution; maximal inequality
UR - http://eudml.org/doc/30671
ER -

References

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