This paper studies the existence and uniqueness of mild solution to stochastic Cahn-Hilliard equations,driven by fractional-colored noise,which is fractional in time and colored in space,with spatial kernel f.A local solution is found by truncating drift term and applying variable substitution to stochastic integral.We prove the tightness of truncated solution by estimating Green function.Finally,a weak convergence of local solution is explored to verify the existence and uniqueness for mild solution of original equation.Coefficient conditions related to Hurst exponent H is then revealed.Furthermore,regularity of the skeleton are checked by applying Cauchy-Schwarz,Burkholder's inequalities and estimating Green function.It makes use of Gronwall's lemma and Girsanov's theorem to reduce large deviation form.We obtain Freidlin-Wentzell inequality in a special space,in which extension of Garsia's lemma plays an important role.The large deviation principle with a small perturbation can then be established.
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