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I am a little confused and would appreciate some elaboration on this. Let $\mu$ be a measure on $\mathbb{R}$ equipped with the Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R})$. Then the translation invariance property of $\mu$ means that \begin{equation} \forall y \in\mathbb{R},\quad\forall B\in\mathcal{B},\quad \mu(y+B)=\mu(B) \end{equation} Now let's say we have the stochastic series $\{x_1,x_2,\cdots,x_T\}$ is a Markov process. Would a transformation of the sort $\{\tilde{x}_1,\tilde{x}_2,\cdots,\tilde{x}_T\}$, where $\tilde{x}_i=x_i+y_i$ for $y_i\in \mathbb{R}$ for $i=1,\cdots,T$ imply that $\{\tilde{x}_1,\tilde{x}_2,\cdots,\tilde{x}_T\}$ also is a Markov process?

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