# What does capital D above an equal sign mean?

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 $$h$$.

• Where did you find this notation?
– Sycorax
Commented Jun 16, 2022 at 2:25
• equality in distribution Commented Jun 16, 2022 at 2:25
• @Sycorax statslab.cam.ac.uk/~rrw1/timeseries/t.pdf page 1. Commented Jun 16, 2022 at 2:30
• @JoeShmo Thanks! It makes sense. Commented Jun 16, 2022 at 2:32
• @Glen_b Thanks for pointing that out. The only problem is, for those people like me who didn't know the meaning of this notation, the search engine is not likely to lead them there. Typing in something like "equal sign with capital d" is to no avail. Commented Jun 16, 2022 at 7:56

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