stochastic kernel equation

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could anyone explain to me the equation (3)? Especially the meaning of the term $z_1(y_1,u_0, z_0), z_0(dx_0),\tau(dx_1|x_0, u_0)$? why $Z_t(\cdot)$ is a Markov chain? What is the equation $3$ saying and the equation before it?

https://doi.org/10.1016/j.sysconle.2019.104512