Method of stochastic normal forms
The paper presents calculations of normal forms for stochastic differential equations in \(\mathbb{R}^ n\) of the form \(\dot x=A(\eta)x+f(x,\eta)+\sigma F(x,\xi(t),\eta)\), where \(A\) is an \(n\times n\)-matrix, \(\xi\) is a stationary mean zero process, \(\eta\) and \(\sigma\) apparently are real paramters, \(f\) and \(A\) are smooth, \(f(0,\eta)\equiv F(0,\xi(t),\eta)\equiv 0\), and for \(\sigma=0\) the system is assumed to undergo a codimension one bifurcation in the parameter \(\eta\) at \(\eta=0\). It seems that further assumptions, in particular on the nature of \(\xi\), are made implicitly later.
stochastic differential equations in \(\mathbb{R}^ n\)
scientific article; zbMATH DE number 92817