On recurrence and transience of multivariate near-critical stochastic processes

[摘要] We obtain complementary recurrence/transience criteria for processes X=(Xn)n≥0 with values in Rd+ fulfilling a non-linear equation Xn+1=MXn+g(Xn)+ξn+1. Here M denotes a primitive matrix having Perron-Frobenius eigenvalue 1, and g denotes some function. The conditional expectation and variance of the noise (ξn+1)n≥0 are such that X obeys a weak form of the Markov property. The results generalize criteria for the 1-dimensional case in [5].

[学科分类] 统计和概率