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We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...

A sequence of random elements $\{X_j,j\in J\}$ is called strongly tight if for an arbitrary $ϵ>0$ there exists a compact set $K$ such that $P\left({\bigcap }_{j\in J}[X_j\in K]\right)>1-ϵ$. For the Polish space valued sequences of random elements we show that almost sure convergence of $\left\{X_n\right\}$ as well as weak convergence of randomly indexed sequence $\left\{X_{\tau }\right\}$ assure strong tightness of $\{X_n,n\in \mathbb{N}\}$. For $L^1$ bounded Banach space valued asymptotic martingales strong tightness also turns out to the sufficient condition of convergence. A sequence of r.e. $\{X_n,n\in \mathbb{N}\}$ is said to converge essentially with...