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Abstract

Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s} G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s} ∫_{ℝ^{n}} H_{τ,z}(x_{τ})q(dτ,dz)$ and $x_{t} - x_{s} ∈ ∫^{t}_{s} F_{τ}(x_{τ})dτ + ∫^{t}_{s}G_{τ}(x_{τ})dw_{τ} + ∫^{t}_{s}∫_{|z|≤1} H_{τ,z}(x_{τ})q(dτ,dz) + ∫^{t}_{s}∫_{|z|>1} H_{τ,z}(x_{τ})p(dτ,dz)$, where p and q are certain random measures, is considered.