Display Custom Post Type Taxonomy Child Categories and their Posts

How can I do this for custom post type taxonomies?

<?php
//get all child categories for category 15, then for each child category display the posts
$parent_cat = 15;
$taxonomy = 'category';
$cat_children = get_term_children( $parent_cat, $taxonomy );

if ($cat_children) {
echo '<p>Category 15</p>';
foreach($cat_children as $category) {
$args=array(
  'cat' => $category,
  'post_type' => 'post',
  'post_status' => 'publish',
  'posts_per_page' => -1,
  'caller_get_posts'=> 1
);
$my_query = null;
$my_query = new WP_Query($args);
if( $my_query->have_posts() ) {
  echo 'List of Posts belonging to Category ' . $category;
  while ($my_query->have_posts()) : $my_query->the_post(); ?>
    <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php     the_title_attribute(); ?>"><?php the_title(); ?></a></p>
    <?php
  endwhile;
}
}
}
wp_reset_query();  // Restore global post data stomped by the_post().
?>