Journal Article10.1007/BF00996931
Switching processes: Averaging principle, diffusion approximation and applications
66
TL;DR: In this paper, a special class of processes with discrete interference of chance-switching processes (SP) is introduced, and limit theorems for these processes in the case of fast switching (averaging principle and diffusion approximation) are proved for the models with simple and semi-Markov switchings.
read more
Abstract: A special class of processes with discrete interference of chance-switching processes (SP), is introduced. The limit theorems for these processes in the case of ‘fast’ switching (averaging principle and diffusion approximation) are proved for the models with simple and semi-Markov switchings. A new approach which is based on the investigation of the asymptotic properties of the special subclass of SP-recurrent process of the semi-Markov type (RPSM), theorems about the convergence of recurrent sequences to the solutions of stochastic differential equations and the convergence of superpositions of random functions is given.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
5.9K
Analysis of Markov Multiserver Retrial Queues with Negative Arrivals
TL;DR: Negative arrivals are used as a control mechanism in many telecommunication and computer networks and the matrix–analytic formalism is used to study the joint distribution of the service facility and the retrial pool, and the approximation by more simple infinite retrial model is proved.
Statistical properties of dynamical chaos
TL;DR: A survey of the results obtained on statistical description of dynamical chaos and the effect of noise on dynamical regimes and regularities of the relaxation to an invariant probability measure for different types of attractors are presented.
•Posted Content
A law of large numbers for limit order books
Ulrich Horst,Michael Paulsen +1 more
TL;DR: A stochastic model of a two-sided limit order book in terms of its key quantities best bid [ask] price and the standing buy [sell] volume density is defined and a limit theorem is proved.
22
Averaging methods for transient regimes in overloading retrial queueing systems
TL;DR: In this article, a new approach is suggested to study transient and stable regimes in overloading retrial queueing systems based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes.
22
References
•Book
Convergence of Probability Measures
Patrick Billingsley
- 01 Jan 1968
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
15K
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
5.9K
Limit Theorems for Stochastic Processes
TL;DR: The authors consider a sequence of processes such that the multivariate distribution of the processes of the process (i.e., the process of finding the distribution of a set of processes) tends to the multi-dimensional distribution of that process.
896
Related Papers (5)
Stewart N. Ethier,Thomas G. Kurtz +1 more
- 04 Apr 1986
V. S. Koroli︠u︡k,Vladimir V. Korolyuk +1 more
- 01 Jan 1999