// hook_menu

$items[] = array('path' => 'my/blog', 'title' => t('My blog'), 'callback' => 'gjg_blog_page', 'callback arguments' => array($user->uid), 'access' => user_access('edit own blog'), 'type' => MENU_CALLBACK);

...

// custom callback function

/**
 * Menu callback; displays users' blog page
 */
function gjg_blog_page($uid) {
  blog_page($uid);
}