mjhjmtu

I have two stocks, A and B. These two "meet" each other at rates q(x), and f(x), by going through a joint-state process called X. Then, A becomes a, and B becomes b.

I thought about visualizing the flowchart as in the attached box. However, I'm clueless as to how solve this within tikz. It'd be best if the arrows are dashed arrows while "inside of X".

With protest, here's as far as I came.

documentclass[border=1in]standalone
usepackagetikz
usetikzlibrarypositioning

tikzstyleblock = [rectangle, draw, fill=blue!20, 
text width=5em, text centered, rounded corners, minimum height=4em]

begindocument
 begintikzpicture
 node [block] (X) X;
 node [block] [below left=of X] (A) A;
 node [block] [above left=of X] (a) a;
 node [block] [below right=of X] (B) B;
 node [block] [above right=of X] (b) b;

 path[->] (A) edge[bend right=90] node [left] (a);
 path[->] (B) edge[bend left=90] node [left] (b);

 endtikzpicture
enddocument

Just divide the path in three if you want the second part dashed.

If you write NodeName.degreee (for example X.130) you can position the end or the beginning of the path exactly where you need. Imagine the node is a circle angle with the east anchor = 0 degrees, so the south anchor is -90, the north = 90, the east = 180, etc.

documentclass[border=1in]standalone
usepackagetikz
usetikzlibrarypositioning
tikzset
 block/.style=
 rectangle, draw, fill=blue!20, 
 text width=5em, text centered, rounded corners, minimum height=4em
 
 

begindocument
 begintikzpicture
 node [block] (X) X;
 node [block] [below left=of X] (A) A;
 node [block] [above left=of X] (a) a;
 node [block] [below right=of X] (B) B;
 node [block] [above right=of X] (b) b;

 draw (A) to[bend right] (X.-130) node[below left=4pt and 5pt] $q(x)$;
 draw[dashed] (X.-130) to[bend right, looseness=.2] (X.130); 
 draw[->] (X.130) to[bend right] (a);

 draw (B) to[bend left] (X.-50) node[below right=4pt and 5pt] $f(x)$;
 draw[dashed] (X.-50) to[bend left, looseness=.2] (X.50);
 draw[->] (X.50) to[bend left] (b);

 endtikzpicture
enddocument

Edit: gorgeous marmot's answer could be simplified without using reverse clipping and putting the straight line behind the X node, like in marya's answer but using on background layer from backgrounds library to not draw it twice.

documentclass[border=1in]standalone
usepackagetikz
usetikzlibrarypositioning,backgrounds
tikzset
 block/.style=
 rectangle, 
 text width=5em, text centered, rounded corners, minimum height=4em, draw, fill=blue!20
 ,
 

begindocument
begintikzpicture
 node[block] (X) X;
 node [block] [below left=of X] (A) A;
 node [block] [above left=of X] (a) a;
 node [block] [below right=of X] (B) B;
 node [block] [above right=of X] (b) b;

 beginscope[on background layer]
 path[->] (A) edge[bend right=90] node[near start, above left] $q(x)$ (a);
 path[->] (B) edge[bend left=90] node[near start, above right] $f(x)$ (b);
 endscope

 beginscope[dashed]
 clip[rounded corners] (X.north west) rectangle (X.south east);
 path[->] (A) edge[bend right=90] (a);
 path[->] (B) edge[bend left=90] (b);
 endscope
endtikzpicture
enddocument

Here is a proposal using reverseclip and use path to draw the dashed path inside and the solid one outside. Please note that tikzstyle is slightly deprecated.

documentclass[border=1in]standalone
usepackagetikz
usetikzlibrarypositioning
makeatletter % https://tex.stackexchange.com/a/38995/121799
tikzset
 use path/.code=pgfsyssoftpath@setcurrentpath#1

makeatother
tikzsetremember path/.style=save path=tmprotect
% https://tex.stackexchange.com/a/12033/121799
tikzsetreverseclip/.style=insert path=(current bounding box.north
 east) rectangle (current bounding box.south west)

tikzsetblock/.style=rectangle, draw, fill=blue!20, 
text width=5em, text centered, rounded corners, minimum height=4em

begindocument
 begintikzpicture
 node [block,save path=pathX] (X) X;
 node [block] [below left=of X] (A) A;
 node [block] [above left=of X] (a) a;
 node [block] [below right=of X] (B) B;
 node [block] [above right=of X] (b) b;

 beginscope
 clip[use path=pathX,reverseclip];
 path[->] (A) edge[bend right=90] (a);
 path[->] (B) edge[bend left=90] (b);
 endscope
 beginscope[dashed]
 clip[use path=pathX];
 path[->] (A) edge[bend right=90] (a);
 path[->] (B) edge[bend left=90] (b);
 endscope

 endtikzpicture
enddocument

Well, the easiest solution I came up is this one

documentclass[border=1in]standalone
usepackagetikz
usetikzlibrarypositioning

tikzstyleblock = [rectangle, draw, fill=blue!20,
text width=5em, text centered, rounded corners, minimum height=4em]

begindocument
 begintikzpicture
 node [block] (X) X;
 node [block] [below left=of X] (A) A;
 node [block] [above left=of X] (a) a;
 node [block] [below right=of X] (B) B;
 node [block] [above right=of X] (b) b;

 path[->] (A) edge[bend right=90] node [left,pos=0.3] $q(r)$ (a);
 path[->] (B) edge[bend left=90] node [right,pos=0.3] $f(r)$ (b);
node [block] (X) X;
path[->,dashed] (A) edge[bend right=90] node [left,pos=0.3] (a);
 path[->,dashed] (B) edge[bend left=90] node [right,pos=0.3] (b);
 endtikzpicture
enddocument