A characterisation of the closure of in
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...
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.
Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution driven by a Wiener process in a Hilbert space in the case when the semigroup is of contraction type.
By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.