# Is there a hierarchy theory for time-bounded Kolmogorov complexity?

We know that there are languages in $$DTIME(n^t)$$ and not in $$DTIME(n^s)$$ for all $$t>s$$ due to simple diagonal arguments (i.e., the Time Hierarchy Theorem), but I'm wondering if there is any equivalent results known for time-bounded Kolmogorov complexity. That is, given polynomials $$p(n)=n^t$$ and $$q(n)=n^s$$ with $$t>s$$ is it always true that for any sufficiently large length $$k$$ there exists a string $$x$$, $$|x|=k$$ such that $$C^p(x)? If this is not true, is it true for $${CD}^p(x)<{CD}^q(x)$$?