What does capital D above an equal sign mean?

Question

I was beginning to self study time series and came across this notation: $\stackrel{\mathcal{D}}{=}$. I wonder what it means? (I have limited access to the textbooks for the moment, so I have to post a question here.)

For more context, it was in the definition for a strongly stationary sequence, where the article states the condition for such a sequence being $(X_{t_1},...,X_{t_k})\stackrel{\mathcal{D}}{=}(X_{t_1+h},...,X_{t_k+h})$ for all $\{t_1,...,t_k\}$ and $h$.

Answer 1

In the context of the linked notes, the symbol refers to equality in distribution ---i.e., the statement:

$$(X_{t_1},...,X_{t_k})\stackrel{\mathcal{D}}{=}(X_{t_1+h},...,X_{t_k+h}) \quad \quad \quad \text{for all } t_1,...,t_k \text{ and } h,$$

is a shorthand way of saying that:

$$\mathbb{P}(X_{t_1},...,X_{t_k} \leqslant \mathbf{x}) = \mathbb{P}(X_{t_1+h},...,X_{t_k+h} \leqslant \mathbf{x}) \quad \quad \quad \text{for all } t_1,...,t_k, h \text{ and } \mathbf{x}.$$