Many prominent continuous-time stochastic volatility models exhibit certain functional relationships between price jumps and volatility jumps. In this paper we construct tests for such relationships in a fairly general context, derive some of their theoretical properties, and investigate their behavior in a simulation study. We apply our tests to three high-frequency data sets from finance. It ...

Given a problem P , one associates to P a degree of unsolvability, i.e., a quantity which measures the amount of algorithmic unsolvability which is inherent in P . We focus on two degree structures: the semilattice of Turing degrees, DT, and its completion, Dw = D̂T, the lattice of Muchnik degrees. We emphasize specific, natural degrees and their relationship to reverse mathematics. We show how ...

Many continuous-time stochastic volatility models exhibit certain functional relationships between jumps in the price and volatility. These relations allow for the construction of tests and, hence, to test these models for high-frequency data. We present such tests in a fairly general context and derive some of their properties. We investigate their behavior in a simulation study. Finally we ap...

For any continuous map f : M → M on a compact manifold M , we define the SRB-like probabilities as a generalization of Sinai-Ruelle-Bowen (i.e. physical) measures. We prove that f has SRB-like measures, even if SRB measures do not exist. We prove that the definition of SRB-like measures is optimal, provided that the purpose of the researcher is to describe the asymptotic statistics for Lebesgue...

The Navier–Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions in the cases of the 2D Rectangle, Cylinder, and Hemisphere. The cases of the 2D Sphere and 2D and 3D Torus are also revisited. MSC2010: 35Q30, 76D03

We study site percolation on Angel & Schramm’s Uniform Infinite Planar Triangulation. We compute several critical and near-critical exponents, and describe the scaling limit of the boundary of large percolation clusters in all regimes (subcritical, critical and supercritical). We prove in particular that the scaling limit of the boundary of large critical percolation clusters is the random stab...

In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider. MSC2010 : 60G51, 60H40, 60H10, 60HXX, 93E20

For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We give an algorithm to compute such bases for one point divisors, and Weierstrass semigroups over an optimal tower of function fields. We also explicitly compute Weierstrass semigroups till level eight. MSC2010 Subject Classificatio...

This paper deals with continuity preservation when minimizing generalized total variation with a L fidelity term or a Dirichlet boundary condition. We extend several recent results for these two types of data terms, mainly by showing comparison principles for the prescribed mean curvature problem satisfied by the level-sets of such minimizers. MSC2010: 49N60, 53A10, 94A08.

We study centre symmetry sets and equidistants for a 1-parameter family of plane curves where, for a special member of the family, there exist two inflexions with parallel tangents. Some results can be obtained by reducing a generating family to normal forms, but others require direct calculation from the generating family. MSC2010 Classification: 57R45, 53A04, 53A15