Printing progress and updates messages SDE problem

function prog_message(dt, u, p, t)
    "Print a message here for the progress bar"
end
solution=solve(problem,SOSRA(),reltol=1e-3,abstol=1e-3,save_everystep = false,progress_true,progress_steps=1000, progress_message = prog_message) 

You can use a DiscreteCallback with condition=true so it launches after each step and just write any function into the affect! to perform the logging. See: