Define a process by its stochastic differential equation :

proc=ItoProcess[\[DifferentialD]x[t]==-x[t] \[DifferentialD]t+Sqrt[1+x[t]^2] \[DifferentialD]w[t],x[t],{x,1},t,w\[Distributed]WienerProcess[]]

Simulate the process :

RandomFunction[proc,{0.,5.,0.01}]

ListLinePlot[%, Filling -> Axis]