Sufficient Conditions For Transience Research Articles

Ergodicity of CIR type SDEs driven by stable processes with random switching

In this paper, we focus on ergodicity and transience of the Cox–Ingersoll–Ross interest rate model driven by stable processes with random switching. Under some assumptions, we prove that the interest rate process and switching process has a unique stationary distribution. In addition, some sufficient conditions for transience of such interest rate model are given.

Ergodic Property of Stable-Like Markov Chains

A stable-like Markov chain is a time-homogeneous Markov chain on the real line with the transition kernel $$p(x,\hbox {d}y)=f_x(y-x)\hbox {d}y$$ , where the density functions $$f_x(y)$$ , for large $$|y|$$ , have a power-law decay with exponent $$\alpha (x)+1$$ , where $$\alpha (x)\in (0,2)$$ . In this paper, under a certain uniformity condition on the density functions $$f_x(y)$$ and additional mild drift conditions, we give sufficient conditions for recurrence in the case when $$0<\liminf _{|x|\longrightarrow \infty }\alpha (x)$$ , sufficient conditions for transience in the case when $$\limsup _{|x|\longrightarrow \infty }\alpha (x)<2$$ and sufficient conditions for ergodicity in the case when $$0<\inf \{\alpha (x):x\in \mathbb {R}\}$$ . As a special case of these results, we give a new proof for the recurrence and transience property of a symmetric $$\alpha $$ -stable random walk on $$\mathbb {R}$$ with the index of stability $$\alpha \ne 1$$ .

Time averages, recurrence and transience in the stochastic replicator dynamics

We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that relates time averages of the process and Nash equilibria of a suitably modified game. Furthermore, a sufficient condition for transience is given in terms of mixed equilibria and definiteness of the payoff matrix. We also present necessary and sufficient conditions for stochastic stability of pure equilibria.

Recurrence-transience criteria for storage processes

It is shown that general storage processes are classified into three types: positive recurrent, null recurrent, and transient processes. Sufficient conditions are given for transience and recurrence (null or positive recurrence), respectively. The sufficient condition for transience is shown to be necessary for transience in a special case (linear release rate case). This is a slight simplification of a known necessary and sufficient condition.

Random walks in a quarter plane with zero drifts: transience and recurrence

In this paper we continue the study of the classification problem for random walks in the quarter plane, with zero drifts in the interior of the domain. The necessary and sufficient conditions for these random walks to be ergodic were found earlier in [3]. Here we obtain necessary and sufficient conditions for transience by constructing suitable Lyapounov functions.

Random walks in a quarter plane with zero drifts: transience and recurrence

In this paper we continue the study of the classification problem for random walks in the quarter plane, with zero drifts in the interior of the domain. The necessary and sufficient conditions for these random walks to be ergodic were found earlier in [3]. Here we obtain necessary and sufficient conditions for transience by constructing suitable Lyapounov functions.

Hendricks libraries and Tsetlin piles

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

Hendricks libraries and Tsetlin piles

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

Transience and recurrence of an interesting Markov chain

This note studies the natural extension to the countable case of a chain considered by Hendricks (1972) and gives necessary and sufficient conditions for transience, null recurrence and positive recurrence.

Transience and recurrence of an interesting Markov chain

This note studies the natural extension to the countable case of a chain considered by Hendricks (1972) and gives necessary and sufficient conditions for transience, null recurrence and positive recurrence.