Align multiline equations at equality sign

Question

I have several (well in this case 2) equations, that I want to align at the equality sign. This is easily done using the align environment from the amsmath package. Additionally, I want to have a note to the far right of each equation, which I do with double ampersands (&&).

My problem is now, what do I do if any of the above-mentioned equations are longer than a single line, i.e. have to be broken up? Right now I have broken them into several environments, but that looks ugly, and not aligned. Any suggestions?

EDIT: I was apparently so hungry that I forgot the MLE, so here it is.

\begin{align*}
Y_{i,k}^{-} = Y_{i-1,k} + &g^0_{k}(Y_{i-1}) \Delta_{i-1,k} + \sum_{j=1}^{d} g^1_{k,j}(Y_{i-1}) \Delta W_{i-1,j} \\&+ \sum_{j_1,j_2=1}^d h_{k,j_1,j_2}(Y_{i-1})(\Delta W_{i-1,j_1}\Delta W_{i-1,j_2}-\Omega_{j_1,j_2}\Delta - A_{i-1,j,k}) && (\mbox{Milstein})
\end{align*}
\begin{align*}
Y_{i,k} &= \begin{cases}
Y_{i,k}^- & \mbox{if } t_{i} \notin \mathcal{I}^k_{arrival} \\
Y_{i,k}^- + Y_{i,k}^- \Delta J_{i,k} & \mbox{if } t_{i} \in \mathcal{I}^k_{arrival} 
\end{cases} && (\mbox{Jump})
\end{align*}

Answer 1

I propose two solutions for the first equation, using \tag. or the second equation, you'll a really centred equationusing \rlap:

\documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[showframe]{geometry}
\usepackage{mathtools}

\begin{document}

\begin{align*}
   & \begin{split}Y_{i,k}^{-} = Y_{i-1,k}&+g⁰_{k}(Y_{i-1}) \Delta_{i-1,k} + ∑_{j=1}^{d} g¹_{k,j}(Y_{i-1}) ΔW_{i-1,j} \\[-1.5ex
    ]&+ \smashoperator{∑_{j₁,j₂=1}^d h_{k,j₁,j₂}}(Y_{i-1})(ΔW_{i-1,j₁}ΔW_{i-1,j₂}-\Omega_{j₁,j₂}Δ- A_{i-1,j,k}) \end{split} \tag{Milstein}
\end{align*}

\begin{multline*}
  Y_{i,k}^{-} = Y_{i-1,k} + g⁰_{k}(Y_{i-1}) \Delta_{i-1,k} + ∑_{j=1}^{d} g¹_{k,j}(Y_{i-1}) ΔW_{i-1,j} \\[-1.5ex]
  + \smashoperator{∑_{j₁,j₂=1}^d h_{k,j₁,j₂}}(Y_{i-1})(ΔW_{i-1,j₁}ΔW_{i-1,j₂}-\Omega_{j₁,j₂}Δ- A_{i-1,j,k}) \tag{Milstein}
\end{multline*}

\begin{align*}
& & Y_{i,k} & = \begin{cases}
    Y_{i,k}^- & \mbox{if } t_{i} ∉ \mathcal{I}^k_\mathrm{arrival} \\
    Y_{i,k}^- + Y_{i,k}^- ΔJ_{i,k} & \mbox{if } t_{i} ∈ \mathcal{I}^k_\mathrm{arrival}
  \end{cases} & & \rlap{(Jump)}
\end{align*}

\end{document}