On the convergence of nonlinear Markov chains (Q1945197)

Let \(X = (X_n^\mu ,n \geqslant 0)\) be a nonlinear Markov chain with an arbitrary state space, initial distribution \({\operatorname{Law}}(X_0^\mu)=\mu\), where \(\mu \) is a probability measure, and transition probabilities \(\operatorname{Pr} (X_{n + 1}^\mu \in B|\; X_n^\mu = x) = \operatorname{P}(x,B,\mu_n)\), where \(\mu_n= {\operatorname{Law}}(X_n^\mu)\). The paper gives sufficient conditions ensuring the existence and uniqueness of a stationary measure, as well as the uniform ergodicity of nonlinear Markov chains.