Well, you can't add styling using pseudo selectors like :hover, :after, :nth-child, or anything like that using jQuery.
If you want to add a CSS rule like that you have to create a <style> element and add that :hover rule to it just like you would in CSS. Then you would have to add that <style> element to the page.
Using the .hover function seems to be more appropriate if you can't just add the css to a stylesheet, but if you insist you can do:
$('head').append('<style>.myclass:hover div {background-color : red;}</style>')
If you want to read more on adding CSS with javascript you can check out
one of David Walsh's Blog posts.