What does this denotation mean? Ito Calculus

Question

there are two denotations which I do not understand. Please note that the two denotation are separate, $X$ in Denotation 1 has nothing related to $X$ in Denotation 2.

Denotation 1: $$dX = \begin{equation*} \begin{bmatrix} dt \\ dR \end{bmatrix} \end{equation*}$$ Where: $$ dR = \mu R dt + \sigma dB$$

Denotation 2: $$dY = \begin{equation*} \begin{bmatrix} dt\\ dX \end{bmatrix} \end{equation*}$$ Where: $$dX = \mu X dt + \sigma X dZ$$

For example in Denotation 1, if $dR$ alone, then I understand the drift and diffusion. But when $dX$ is expressed in form of matrix here, I am a little bit confuse. how to inteprete $dX$ (in Denotation 1) and $dY$ (in Denotation 2) Thank you

Answer 1

For both notations

Denotation 1: $$dX = \begin{equation*} \begin{bmatrix} dt \\ dR \end{bmatrix} \end{equation*}$$ Where: $$ dR = \mu R dt + \sigma dB$$

they probably just meant it in vector notation $dX=[dX_{1},dX_{2}]$ and so eg. in notation 1 we have

$$dX_{1}=dt \text{ and }dX_{2}=dR=\mu R dt + \sigma dB.$$