Phenomenological and ratio bifurcations of a class of discrete time stochastic processes (Q652421)

The authors study classification problems for Markov processes of the following form: We have \[ X_{t+1}= f_\mu(X_t)+ \varepsilon_t, \] where \(f_\mu: \mathbb{R}^m\to\mathbb{R}^m\) is a parametrized family of \(C^k\)-maps, \(k\geq 2\), and the sequence \((\varepsilon_t)\) consists of independent identically distributed normal random variables. Such processes are called stochastic dynamical systems.