123590583
On badly approximable numbers
122160425
Correction to on Thue's equation
120328164
Irregularities of distribution. IV
129296972
Irregularities of distribution. V
120616848
Stetige Funktionen auf dem Torus.
121229043
Some results in probabilistic geometry
121309269
Stochastic Integration for Some Rough Non‐adapted Processes
For the Wiener process W on the unit interval and 0 ⩽ θ ⩽ 1/4 consider the non-adapted process ut =sgn(Wt−θ)sgn(W1−WT+θ), θ⩽t⩽1−θ. By giving explicit descriptions of their expansions in terms of generalized Hermite polynomials we show that they possess Skorohod integral processes. In the more interesting case θ = 0, a component due to the interaction of forwards and backwards Wiener process seems to dominate the non-interaction part, whereas for θ > 0 interaction drops geometrically with respect to non-interaction. We translate these purely analytic properties into more familiar terms of samples of stochastic processes. Firstly, we construct simple approximations of the integral process which are of the type of Riemann sums. We then show that their quadratic variations are the same as for the Wiener process on [θ, 1 − θ]. Finally, using the fact that W remains a semimartingale if its filtration is enlarged by W1, we compare the resulting Ito integral process to the Skorohod integral process of u in case θ = 0. We show that they differ by a local time. Consequently the Skorohod integral process of u is a semimartingale.
121073876
Existence of solutions of certain nonconvex optimal control problems governed by nonlinear integral equations
Optimal control problems with nonlinear equations usually do not have a solution, i.e. an optimal control. Nevertheless, if the cost functional is uniformly concave with respect to the state, the solution may exist. Using the Balder's technique based on a Youngmeasure relaxation, Bauer's external principle and investigation of extreme Young measures; the existence is demonstrated here for optimal control processes described by nonlinear integral equations
120957526
On Stochastic Differential Equations with Reflecting Barriers
1555430
On a general class of one-factor models for the term structure of interest rates

Abstract.We propose a general one-factor model for the term structure of interest rates which based upon a model for the short rate. The dynamics of the short rate is described by an appropriate function of a time-changed Wiener process. The model allows for perfect fitting of given term structure of interest rates and volatilities, as well as for mean reversion. Moreover, every type of distribution of the short rate can be achieved, in particular, the distribution can be concentrated on an interval. The model includes several popular models such as the generalized Vasicek (or Hull-White) model, the Black-Derman-Toy, Black-Karasinski model, and others. There is a unified numerical approach to the general model based on a simple lattice approximation which, in particular, can be chosen as a binomial or 
$N$-nomial lattice with branching probabilities 
$1/N$.

120009511
On semimartingale diffusions and stochastic differential equations
Given a regular diffusion X on the real axis which is a semimartingale we describe the semimartingale decomposition of X. We then give necessary and sufficient conditions in terms of the scale and the speed measure for X being a solution of an Ito type stochastic differential equation driven by a Wiener process and with classical drift or a drift term involving the local time of X. A regular diffusion is also characterized as unique solution of a certain martingale problem. Finally we discuss an example related to skew Brownian motion