Classic editor

You can use the filter hook page_attributes_dropdown_pages_args and set authors parameter in query arguments.

add_filter( 'page_attributes_dropdown_pages_args', 'se343814_own_post_as_post_parent', 10, 2 );

function se343814_change_post_type_args( $dropdown_args, $post )
{
    //
    // for which types to apply the filter
    if ( $post->post_type != 'page' )
        return $dropdown_args;

    $dropdown_args['authors'] = get_current_user_id();

    return $dropdown_args;
}

Block editor

In the case of a block editor, above solution will not work.
The list of posts that can be set as a parent is retrieved by a REST request, with context parameter set to edit.
I do not know if it’s possible to change the request data when initializing the editor, probably there is no such filter.

However, you can use the rest_{$post_type}_query filter in conjunction with the context that is set in the request.

add_filter( 'rest_page_query', 'se343814_rest_own_post_as_post_parent' , 10, 2 );

function se343814_rest_query_page_parent( $args, $request )
{
    //
    // apply filter only when editing the post
    if ( ! isset($request['context']) || $request['context'] != 'edit' )
        return $args;

    if ( empty($args['author']) )
        $args['author'] = get_current_user_id();

    return $args;
}