  In the present paper, we give some examples of stochastic differential
equations which have delicateness in the Markov and strong Markov properties,
the uniqueness locally in time and globally in time, and initial conditions.
Moreover, we show that such stochastic differential equations appear in the
limits of stochastic differential equations which have the existence and
pathwise uniqueness of solutions. These examples are constructed in motivation
to singular stochastic partial differential equations. We also give some
examples of shifted equations whose sum of the solutions depends on the choices
of the decomposition of the initial condition of the original equation.
