An analysis expression for the stationary probability distribution of asymmetric superconducting quantum interference device with two Josephson junctions (dc SQUID) driven by thermal noise is derived from two-dimensional Fokker-Planck equation, where the potential condition is satisfied. Two of the three asymmetric parameters, inductance asymmetric parameter η and critical current asymmetric parameter a, can be changed in this condition, but resistance asymmetric parameter ρ cannot be changed. The "ripple" phenomenon of circulating current ca...