Spitzer’s Formula Involving Capacity

TL;DRAbstract

Let X t be a strongly transient Lévy process on a second countable locally compact Abelian group and let B be a bounded Borel set. Set E B (t,A)=∫Px(T B ≤t, $${{\rm X}_{{T_B}}}$$ ∈A)dx where T B =inf{t >0:X t ∈B} We give an asymptotic expansion to third order for E B (t, A). If X t is a strongly transient strictly stable process on R d we give an expansion to order 4 of E B (t,R d ).

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