If one can show that the process converges to a stationary process in probability, does it mean that the process is ergodic?
2026-03-31 03:30:49.1774927849
Ergodicity of stochastic process
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If a process converges to a "unique" stationary process, then it should be ergodic. But as you say it converges to a stationary process in probability, it should also imply that it is unique and therefore ergodic as well.