If $x$ is a vertex of a digraph $D$, then we denote by $d^+(x)$ and $d^-(x)$ the outdegree and the indegree of $x$, respectively. A digraph $D$ is called regular, if there is a number $p \in \mathbb{N}$ such that $d^+(x) = d^-(x) = p$ for all vertices $x$ of $D$. A $c$-partite tournament is an orientation of a complete $c$-partite graph. There are many results about directed cycles of a given length or of directed cycles with vertices from a given number of partite sets. The idea is now to combine the two properties. In this article, we examine in particular, whether $c$-partite tournaments with $r$ vertices in each partite set contain a cycle with exactly $r-1$ vertices of every partite set. In 1982, Beineke and Little [2] solved this problem for the regular case if $c = 2$. If $c \ge 3$, then we will show that a regular $c$-partite tournament with $r \ge 2$ vertices in each partite set contains a cycle with exactly $r-1$ vertices from each partite set, with the exception of the case that $c = 4$ and $r = 2$.
.In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept of causality between stochastic processes, which is based on Granger's definition of causality. Also, we provide applications of our results to solutions of some stochastic differential equations.