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We consider the continuous parabolic Anderson model with the Gaussian fieldsunder the measure-valued initial conditions, the covariances of which arenonhomogeneous in time and fractional rough in space. We mainly study thespatial behaviors for the Feynman-Kac formulas in Stratonovich's sense.Benefited from the application of Feynman-Kac formula based on Brownian bridge,the precise spatial asymptotics can be obtained in the broader conditions thanbefore.

Spatial asymptotics for the Feynman-Kac formulas driven by  time-dependent and space-fractional rough Gaussian fields with the  measure-valued initial data