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The aim of this paper is to study the continuity correction for barrier options in jump-diffusion models. For this purpose, we express the pay-off of a barrier option in terms of the maximum of the un...
The Lyapunov exponents of locally constant GL(2, C)-cocycles over Bernoulli shifts depend continuously on the cocycle and on the invariant probability. The Oseledets decomposition also depends continu...
For a class of partially hyperbolic Ck, k > 1 diffeomorphisms with circle center leaves we prove existence and finiteness of physical (or Sinai-Ruelle-Bowen) measures, whose basins cover a full Lebesg...
We consider a family of non-evolutionary partial differential equations known as Holm - Staley b - family which includes the integrable Camassa-Holm and Degasperis-Procesi equations. We show that the ...
For a Radon measure $\mu$ on $\bbR,$ we show that $L^{\infty}(\mu)$ is invariant under the group of translation operators $T_t(f)(x) = {$f(x-t)$}\ (t \in \bbR)$ if and only if $\mu$ is equivalent to ...
We consider the Schr\"odinger operator $H = -\Delta + V$ in a layer or in a $d$-dimensional cylinder. The potential $V$ is assumed to be periodic with respect to some lattice. We establish the absolu...
We consider averages  of spectral measures of rank one perturba-tions with respect to a -finite measure . It is examined how various degrees of continuity of  with respect to -dimensional Hausdor...
This paper is concerned with H¨older regularity of viscosity solutions of second-order, fully non-linear elliptic integro-differential equations. Our results rely on two key ingredients: first we ass...
A manifold M with a foliation F is minimizable if there exists a Riemannian metric g on M such that every leaf of F is a minimal submanifold of (M, g).
The Pseudo-Differential Operator (p.d.o.) hμ,a associated with the Bessel Operator involving the symbol a(x, y) whose derivatives satisfy certain growth conditions depending on some increasing sequenc...
It was already known that a p-adic, locally Lipschitz continuous semialgebraic function is piecewise Lipschitz continuous, where the pieces can be taken semi-algebraic.
We consider the Itˆo SDE with non-degenerate diffusion coefficient and measurable drift coefficient. Under the condition that the gradient of the diffusion coefficient and the divergences of the...
We obtain sharp bounds for the modulus of continuity of the uncentered maxi-mal function in terms of the modulus of continuity of the given function, via integral formulas.
When considering regularity of surfaces, it is its geometry that is of interest. Thus, the concept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this pa...
We give a construction of the Floer homology of the pair of vnon-compact Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy that moves the infinity but ...

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