We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to evolution interacting particle systems, which leads a general class fractional kinetic measure-valued evolutions with variable order. prove well-posedness resulting new equations and present probabilistic formula for their solutions. Though our method are quite general, simplicity we treat in detail only ve...

We introduce a new concept of dissipative measure-valued martingale solutions to the stochastic compressible Euler equations. These are weak in probabilistic sense i.e., probability space and driving Wiener process an integral part solution. derive relative energy inequality for equations and, as corollary, we exhibit pathwise weak-strong uniqueness principle. Moreover, making use inequality, i...