ItoProcess[
  {
    \[DifferentialD]s[1,t]==\[DifferentialD]\[Eta][t]+\[DifferentialD]t s[1,t],
    \[DifferentialD]u[1,t]==2 \[DifferentialD]\[Eta][t]+2 \[DifferentialD]t u[1,t],
    \[DifferentialD]x[1,t]==3 \[DifferentialD]\[Eta][t]+3 \[DifferentialD]t x[1,t],
    \[DifferentialD]s[2,t]==4 \[DifferentialD]\[Eta][t]+4 \[DifferentialD]t s[2,t],
    \[DifferentialD]u[2,t]==5 \[DifferentialD]\[Eta][t]+5 \[DifferentialD]t u[2,t],
    \[DifferentialD]x[2,t]==6 \[DifferentialD]\[Eta][t]+6 \[DifferentialD]t x[2,t]
  },{
    s[1,t],u[1,t],x[1,t],s[2,t],u[2,t],x[2,t]
  },{
    {s[1],u[1],x[1],s[2],u[2],x[2]},{0,0,0,0,0,0}
  },t,\[Eta]\[Distributed]WienerProcess[0,1]
]