In this paper, we deal with a class of backward stochastic differential equations driven by Teugels martingales associated with a Lévy process (BSDELs). The comparison theorem is obtained. It is also shown that the solution of BSDE provides a viscosity solution of the associated system with partial integro-differential equations.

In fluorescence fluctuation polarization sensitive experiments, the limitations associated with detecting the rotational timescale are usually eliminated by applying fluorescence correlation spectroscopy analysis. In this paper, the variance of the time-averaged fluorescence intensity extracted from the second moment of the measured fluorescence intensity is analyzed in the short time limit, be...

In this paper we use viscosity solution methods to show that almost integrable Hamiltonian systems are not smoothly integrable at rotation numbers which are exponentially close to resonances.

T he UK Parliament recently debated and then approved legislation to allow mitochondrial replacement (MR) to be used in the clinic. However, we are concerned that some of the science of MR has been misunderstood or otherwise given only fleeting consideration. We set out our arguments below and offer a way forward to ensure that MR can safely deliver the health benefits it promises for those suf...

1 Who knoWs a utility representation Repeatedly it is alleged that this or that theory concerns a decision maker maximizing some utility function. But, as I have been at pains to discuss, the representation is not a creature of the decision maker but of the scientist studying the decision maker’s behavior “The representation theorems go in only one direction: from behavioral and structural prop...