In [16] we obtained a nonconventional invariance principle (functional central limit theorem) for sufficiently fast mixing stochastic processes with discrete and continuous time. In this paper we derive a nonconventional invariance principle for sufficiently well mixing random fields.

We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold.

We derive an invariance principle for the lift to rough path topology of stochastic processes with delayed regenerative increments under optimal moment condition. An interesting feature result is emergence area anomaly, a correction term in second level limiting which identified as average on regeneration interval. A few applications include random walks environment and additive functionals rec...

In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. particular, assuming existence of a K-invariant measure μ with full support, show that conditional definiteness kernel K is equivalent to long list other properties: including, among others, convexity functional, inequalities for mixed energies, fact minimizes integral in various sen...

Geometrical invariance, in particular affine invariance, has been recently proposed as an important principle underlying the production of hand movements. However, tests of affine invariance have traditionally been applied to the consequences of this principle rather to the principle itself. Here, we designed and performed an original, direct, test of affine invariance in a scribbling experimen...