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A generalization of the conservation integral

Volkmar Liebscher (1998)

Banach Center Publications

Starting from the scheme given by Hudson and Parthasarathy [7,11] we extend the conservation integral to the case where the underlying operator does not commute with the time observable. It turns out that there exist two extensions, a left and a right conservation integral. Moreover, Itô's formula demands for a third integral with two integrators. Only the left integral shows similar continuity properties to that derived in [11] used for extending the integral to more than simple integrands. In...

A note on maximal estimates for stochastic convolutions

Mark Veraar, Lutz Weis (2011)

Czechoslovak Mathematical Journal

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.

A note on maximal inequality for stochastic convolutions

Erika Hausenblas, Jan Seidler (2001)

Czechoslovak Mathematical Journal

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.

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