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Let $S$ be a ring of polynomials in finitely many variables over a field. Inthis paper we give lower bounds for depth and Stanley depth of modules of thetype $S/I^t$ for $t\geq1$, where $I$ is the edge ideal of some caterpillar andlobster trees. These new bounds are much sharper than the existing bounds forthe classes of ideals we considered.

Depth and Stanley depth of powers of the edge ideals of some caterpillar and lobster trees