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We consider one-dimensional stochastic equations involving local times of unknown processes. We interpret these equations as diffusion in layered media with semi-permeable barriers and we study the limit behavior of solutions as barriers compress in one barrier. Conditions for convergence in law and limit equation are obtained.

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The paper deals with an integral functional on a stationary random mixing field and on a solution of the stochastic equation which depend on a small parameter. The type of the functional is conditioned by the probabilistic representation of solutions of the Cauchy problem and the first boundaryvalue problem for a linear second-order parabolic equation in a nondivergent form with unbounded quick random oscillations of the zero-order term of the derivative. The central limit theorem of convergence of the functional is proved.