This paper first introduces a refined version of the Azuma-Hoeffding inequality for discrete-parameter martingales with uniformly bounded jumps. The refined inequality is used to revisit the large deviations analysis of binary hypothesis testing.

We prove two martingale identities which involve exit times of Lévy-driven Ornstein–Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption that positive jumps of the Lévy process are exponentially distributed.

This paper proposes a new test for the presence of jumps in asset prices. The test is derived from a direct application of Itô’s lemma to the semi-martingale process of asset prices. Intuitively, the proposed test measures the impact of jumps on the third and higher order return moments and is also directly related to the profit/loss function of a variance swap replication strategy. We derive i...

Many studies have been conducted on the characteristics of hydraulic jumps over horizontal basins. On sloping basins, however, few such studies have been performed so that the issue requires more investigation. A significant number of studies has also been conducted on basins with positive slopes but comparatively few have been carried out on basins with negative slopes. This study was carried ...

We give a short summary of Varopoulos’ generalised Hardy-LittlewoodSobolev inequality for self-adjoint C0 semigroups and give a new probabilistic representation of the classical fractional integral operators on Rn as projections of martingale transforms. Using this formula we derive a new proof of the classical Hardy-LittlewoodSobolev inequality based on Burkholder-Gundy and Doob’s inequalities...