Let C⊆L0+ be convex, and let g∈C be strictly positive on C. Assume that csg(C) is bounded. To complete the proof of Theorem 1.4, we have to establish that g∈Cnum. In order to ease the reading and understanding, we split the proof in four steps.

Our algorithm for non-monotone DR-submodular maximization is shown in Algorithm 2. We obtain the value M by guessing like in the monotone case. Unlike the monotone case, we now include the constraints →x≤(1−ϵ)→1 into the matrix A, i.e., we solve the…

For helpful comments, we thank Bruno Bouchard, Yan Dolinsky, Ioannis Karatzas, Kostas Kardaras, Johannes Muhle-Karbe, Teemu Pennanen, Walter Schachermayer, Mete Soner, and seminar participants at the Oberwolfach Workshop in Stochastic Analysis in Fi…

We now give the proofs of the main results stated in Section 3. In all the proofs below, the letters c, c1,c2,… will denote positive constants whose values can change from line to line.

The proof of one implication of Theorem 1.1 is easy and somewhat classic, but will be presented anyhow here for completeness. Start by assuming the existence of an ELMD Z and pick any sequence (Xk)k∈N of wealth processes in X such that limk→∞Xk(0)=0…

First, recall that to any self-decomposable distribution X there corresponds a Lévy process L such that

Through our work correlating radio sources from the FIRST survey with optical data from the SDSS, we identified hundreds of clusters associated with bent-double radio sources at low-to-moderate redshift. In addition, we found 653 bent radio sources …

In this work, we presented a novel method to construct a volume preserving mapping from a cube to any given solid model. By selecting a solid cube as our canonical domain of interest, the process of volumetric meshing yields a regular hexahedral str…