Krylov-Veretennikov formula for functionals from the stopped Wiener process

We consider a class of measures absolutely continuous with respect to the distribution of the stopped Wiener process $w(\cdot\wedge\tau)$. Multiple stochastic integrals, that lead to the analogue of the It\^o-Wiener expansions for such measures, are described. An analogue of the Krylov-Veretennikov formula for functionals $f=\varphi(w(\tau))$ is obtained

Measurement of Hadronic Resonances with ALICE at the LHC

The ALICE experiment has measured production of hadronic resonances such a

Statistical analysis of high-speed jet flows

The spatiotemporal dynamics of pressure fluctuations of a turbulent jet flow is examined from the viewpoints of symbolic permutations theory and Kolmogorov-Smirnov statistics. The methods are applied to unveil hidden structures in the near-field of the two jets corresponding to the NASA SHJAR SP3 and SP7 experiments. Large Eddy Simulations (LES) are performed using the high-resolution Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) accelerated on Graphics Processing Units (GPUs). It is demonstrated that the decomposition of the LES pressure solutions into symbolic patterns of simpler temporal structure reveals the existence of some orderly structures in the jet flows. To separate the non-linear dynamics of the revealed structures from the linear part, the results based on the pressure signals obtained from LES are compared with the surrogate dataset constructed from the original data