Stochastic Convolutions Driven by Martingales: Maximal Inequalities and Exponential Integrability

A note on maximal estimates for stochastic convolutions

“…Our methods to obtain continuity results are based on techniques similar to the ones in [6], [16], [17]. The results are comparable with [6] but are of independent interest.…”

“…We will be interested in obtaining conditions for path-continuity of the stochastic convolution where G : R + × Ω → L (H, X) is such that the stochastic integral with respect to the cylindrical Brownian motion W H exists. There are many such continuity results in literature (see [4], [6], [9], [16], [17], [27] and references therein).…”

“…The proof of Theorem 1.1 will be given in Section 2 and uses a dilation argument in a spirit similar to [16], [17]. However, the enlargements of the spaces we need to consider are more complicated.…”

“…[6], [17] and references therein) for sup t 0 S ⋄ G(t) . This is indeed the case as follows from the next result.…”

Existence of Lévy term structure models

“…The idea to use the Szeköfalvi-Nagy's theorem on unitary dilations in order to overcome the difficulties arising from stochastic convolutions, is due to Hausenblas and Seidler, see [31] and [30].…”