Coupling the Kolmogorov diffusion: maximality and efficiency considerations

Optimally Coupling the Kolmogorov Diffusion, and Related Optimal Control Problems

We discuss the optimal Markovian coupling before an exponential time of the Kolmogorov diffusion, and a class of related stochastic control problems in which the aim is to hit the origin before an exponential time. We provide a scaling argument for the optimal control in the near field and use rational WKB approximation to obtain the optimal control in the far field, and compare these analytica...

analysis the diffusion process for polymer solution using FTIR-ART technique: special considerations

Spurious diffusion in particle simulations of the Kolmogorov flow

Particle simulations of the Kolmogorov flow are analyzed by the LandauLifshitz fluctuating hydrodynamics. It is shown that a spurious diffusion of the center of mass corrupts the statistical properties of the flow. The analytical expression for the corresponding diffusion coefficient is derived. Some fifty years ago, Kolmogorov introduced a simple hydrodynamic model, that displays various insta...

Deflationism, Conservativeness and Maximality

This schema, restricted in some way in order to avoid the paradoxes, is said to capture the whole content of our intuitive notion of truth. In effect truth is called sometimes a “purely logical” device a predicate devoid of content, which doesn’t express any substantial relation between our language and the world. According to one proposal, conservativeness is a good explication of this “conten...

Invariant Maximality and Incompleteness

We present new examples of discrete mathematical statements that can be proved from large cardinal hypotheses but not within the usual ZFC axioms for mathematics (assuming ZFC is consistent). These new statements are provably equivalent to Π1 sentences (purely universal statements, logically analogous to Fermat's Last Theorem) in particular provably equivalent to the consistency of strong set t...