How do I stream objects of incompatible types into a list?

return list.stream()
           .filter(Student.class::isInstance)
           .map(Student.class::cast)
           .collect(Collectors.toList());

It should be a cast there, otherwise, it's still a Stream<Person>. The instanceof check doesn't perform any cast.

Student.class::isInstance and Student.class::cast is just a preference of mine, you could go with p -> p instanceof Student and p -> (Student)p respectively.

You need a cast:

public static List<Student> findStudents(List<Person> list) 
{
    return list.stream()
               .filter(person -> person instanceof Student) 
               .map(person -> (Student) person)
               .collect(Collectors.toList());
}

Another alternative.

public static List<Student> findStudents(List<Person> list) 
{
    return list.stream()
            .filter(s -> Student.class.equals(s.getClass()))
            .map(Student.class::cast)
            .collect(Collectors.toList());
}