Strong and weak solutions to stochastic inclusions

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Institute of Mathematics, Higher College of Engineering, Podgórna 50, 65-246 Zielona Góra, Poland

Existence of strong and weak solutions to stochastic inclusions

x_{t} - x_{s} \in \int^{t}_{s} F_{τ} (x_{τ}) d τ + \int^{t}_{s} G_{τ} (x_{τ}) d w_{τ} + \int^{t}_{s} \int_{ℝ^{n}} H_{τ, z} (x_{τ}) q (d τ, d z)

and

x_{t} - x_{s} \in \int^{t}_{s} F_{τ} (x_{τ}) d τ + \int^{t}_{s} G_{τ} (x_{τ}) d w_{τ} + \int^{t}_{s} \int_{| z | \leq 1} H_{τ, z} (x_{τ}) q (d τ, d z) + \int^{t}_{s} \int_{| z | > 1} H_{τ, z} (x_{τ}) p (d τ, d z)

, where p and q are certain random measures, is considered.

strong and weak solutions, stochastic inclusions

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