LetX(1)={X(1)(s),s∈R+}andX(2)={X(2)(t),t∈R+}betwoindependentnondegeneratediusionprocesseswithvaluesinRd.TheexistenceandfractaldimensionofintersectionsofthesamplepathsofX(1)andX(2)arestudied.Moregenerally,letE1,E2■(0,∞)andFRdbeBorelsets.AnecessaryconditionandasuffcientconditionforP{X(1)(E1)∩X(2)(E2)∩F=φ}>0areprovedintermsoftheBessel-RiesztypecapacityandHausdormeasureofE1×E2×Finthemetricspace(R+×R+×Rd,ρ),whereρisanunsymmetricmetricdefinedinR+×R+×Rd.Underreasonableconditions,resultsresemblingthoseofBrowianmotionareobtained.
