On the strong stability of ergodic iterations
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for any other initialization, the difference between the two processes converges to zero almost surely. Under some mild conditions on the corresponding recursive map, without any condition on the driving sequence, we show the strong stability of iterations. Several applications are surveyed such as generalized autoregression and queuing. Furthermore, new results are deduced for Langevin-type iterations with dependent noise and for multitype branching processes.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Affine Jump-Diffusions: Stochastic Stability and Limit Theorems
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such …
parameter estimationUniform-in-Time Wasserstein Stability Bounds for (Noisy) Stochastic Gradient Descent
Algorithmic stability is an important notion that has proven powerful for deriving generalization bounds for practical algorithms. The last decade has witnessed an increasing number of stability bounds for different algo…
Generalization BoundsLearning TheoryStochastic OptimizationLog-Ergodic Dynamics in Stochastic Monetary Velocity: Theoretical Insights and Economic Implications
We suggest employing log-ergodic processes to simulate the velocity of money in an ergodic manner. Our approach sheds light on economic behavior, policy implications, and financial dynamics by maintaining long-term stabi…
Convergence of Finite Memory Q-Learning for POMDPs and Near Optimality of Learned Policies under Filter Stability
In this paper, for POMDPs, we provide the convergence of a Q learning algorithm for control policies using a finite history of past observations and control actions, and, consequentially, we establish near optimality of …
Q-LearningLearning Expected Reward for Switched Linear Control Systems: A Non-Asymptotic View
In this work, we show existence of invariant ergodic measure for switched linear dynamical systems (SLDSs) under a norm-stability assumption of system dynamics in some unbounded subset of $\mathbb{R}^{n}$. Consequently, …