On recurrence and transience of multivariate near-critical stochastic processes

@article{Kersting2016OnRA,
  title={On recurrence and transience of multivariate near-critical stochastic processes},
  author={G{\"o}tz Kersting},
  journal={arXiv: Probability},
  year={2016}
}
  • G. Kersting
  • Published 13 May 2016
  • Mathematics
  • arXiv: Probability
We obtain complementary recurrence and transience criteria for processes $X=(X_n)_{n \ge 0}$ with values in $\mathbb R^d_+$ fulfilling a non-linear equation $X_{n+1}=MX_n+g(X_n)+ \xi_{n+1}$. Here $M$ denotes a primitive matrix having Perron-Frobenius eigenvalue 1, and $g$ denotes some function. The conditional expectation and variance of the noise $(\xi_{n+1})_{n \ge 0}$ are such that $X$ obeys a weak form of the Markov property. The results generalize criteria for the 1-dimensional case in [5… 
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References

SHOWING 1-10 OF 10 REFERENCES
Recurrence and Transience of Near-Critical Multivariate Growth Models: Criteria and Examples
We consider stochastic processes (X n )n ≥ 0 taking values in \(\mathbb{R}_{+}^{d} =\{ (x_{1},\ldots,x_{d})^{T} \in \mathbb{R}^{d}: x_{i} \geq 0\}\), i.e. the d-dimensional orthant, and adapted to
On recurrence and transience of growth models
Let Xn be non-negative random variables, possessing the Markov property. We given criteria for deciding whether Pr(X. -- oo) is positive or 0. It turns out that essentially this depends on the
Criteria for the recurrence or transience of stochastic process. I
Criterion for unlimited growth of critical multidimensional stochastic models
  • E. Adam
  • Mathematics
    Advances in Applied Probability
  • 2016
TLDR
A criterion for unlimited growth with positive probability for a large class of multidimensional stochastic models and recovers the necessary and sufficient conditions for recurrence and transience for critical multitype Galton–Watson with immigration processes.
On the unlimited growth of a class of homogeneous multitype Markov chains
mota@unex.esWe consider a homogeneous multitype Markov chain whose states have non-negative integercoordinates, and give criteria for deciding whether or not the chain grows indefinitely with
Probability: Theory and Examples
This book is an introduction to probability theory covering laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a
Non-negative Matrices and Markov Chains
Finite Non-Negative Matrices.- Fundamental Concepts and Results in the Theory of Non-negative Matrices.- Some Secondary Theory with Emphasis on Irreducible Matrices, and Applications.- Inhomogeneous
Matrix analysis
TLDR
This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.