On an invariance principle for phase separation lines
On asymptotic behaviour of empirical processes
On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions
On fully coupled continuous time random walks
Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.
On Functional of Order Statistics.
On homogenization of space-time dependent and degenerate random flows II
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle is proved for the critical rescaling of the diffusion. Here, we generalize this approach to diffusions whose space-time scaling differs from the critical one.
On non-ergodic versions of limit theorems
The author investigates non ergodic versions of several well known limit theorems for strictly stationary processes. In some cases, the assumptions which are given with respect to general invariant measure, guarantee the validity of the theorem with respect to ergodic components of the measure. In other cases, the limit theorem can fail for all ergodic components, while for the original invariant measure it holds.
On processes with conditional independent increments and stable convergence in law
On the Asymptotic Behaviour of Linear Learning Processes with Partial Forgetting.
On the convergence of stochastic integrals driven by processes converging on account of a homogenization property.
On the functional central limit theorem for stationary processes
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments
Let Fn be the empirical distribution function (df) pertaining to independent random variables with continuous df F. We investigate the minimizing point of the empirical process Fn - F0, where F0 is another df which differs from F. If F and F0 are locally Hölder-continuous of order α at a point τ our main result states that converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous Poisson-process with a drift. The time-transformation...
On the Power of Nonparametric Changepoint-Tests.
On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
Ordered random walks.