Will caught Pokemons got their stats improve if their trainer level up?

Yeah, the pokemons' stats will rise with your level. It's also good to note that the max CP of the pokemon will also rise.

Their max level (hidden) will go up, meaning you can level them up farther. The meter that is displayed by their current level/cp progress as against their current max level/cp will show the fill recede. But nothing else changes, though some people claim their eggs have statted up as they have leveled themselves up.