Canonical correlation analysis for functional data

Mirosław Krzyśko; Łukasz Waszak

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Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{ℝ^{n}} H_{τ, z} (x_{τ}) q (d τ, d z)$ and $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{| z | \leq 1} H_{τ, z} (x_{τ}) q (d τ, d z) + \int_{s}^{t} \int_{| z | > 1} H_{τ, z} (x_{τ}) p (d τ, d z)$ , where p and q are certain random measures, is considered.