Weak convergence of Markov-modulated diffusion processes with rapid switching

2014 ◽  
Vol 86 ◽  
pp. 74-79 ◽  
Author(s):  
Gang Huang ◽  
Michel Mandjes ◽  
Peter Spreij
Keyword(s):  
Weak Convergence ◽  
Diffusion Processes ◽  
Markov Modulated ◽  
Rapid Switching

scholarly journals Large deviations for Markov-modulated diffusion processes with rapid switching

2016 ◽  
Vol 126 (6) ◽  
pp. 1785-1818 ◽  
Author(s):  
Gang Huang ◽  
Michel Mandjes ◽  
Peter Spreij
Keyword(s):  
Large Deviations ◽  
Diffusion Processes ◽  
Markov Modulated ◽  
Rapid Switching

scholarly journals Weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain

2021 ◽  
Vol 58 (2) ◽  
pp. 372-393
Author(s):  
H. M. Jansen
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
The State ◽  
Stochastic Integrals ◽  
Occupation Measure ◽  
Generator Matrix ◽  
Markov Modulated ◽  
Erlang Loss

AbstractOur aim is to find sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure of a Markov chain. First, we study properties of the state indicator function and the state occupation measure of a Markov chain. In particular, we establish weak convergence of the state occupation measure under a scaling of the generator matrix. Then, relying on the connection between the state occupation measure and the Dynkin martingale, we provide sufficient conditions for weak convergence of stochastic integrals with respect to the state occupation measure. We apply our results to derive diffusion limits for the Markov-modulated Erlang loss model and the regime-switching Cox–Ingersoll–Ross process.

Weak convergence of symmetric diffusion processes

1997 ◽  
Vol 109 (2) ◽  
pp. 159-182 ◽  
Author(s):  
Kazuhiro Kuwae ◽  
Toshihiro Uemura
Keyword(s):  
Weak Convergence ◽  
Diffusion Processes ◽  
Symmetric Diffusion

scholarly journals DIFFUSION LIMITS FOR A MARKOV MODULATED BINOMIAL COUNTING PROCESS

2019 ◽  
Vol 34 (2) ◽  
pp. 235-257
Author(s):  
Peter Spreij ◽  
Jaap Storm
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
Regime Switching ◽  
Limit Theorems ◽  
Counting Process ◽  
Limit Behavior ◽  
Diffusion Approximations ◽  
Default Rate ◽  
Markov Modulated ◽  
Rapid Switching

In this paper, we study limit behavior for a Markov-modulated binomial counting process, also called a binomial counting process under regime switching. Such a process naturally appears in the context of credit risk when multiple obligors are present. Markov-modulation takes place when the failure/default rate of each individual obligor depends on an underlying Markov chain. The limit behavior under consideration occurs when the number of obligors increases unboundedly, and/or by accelerating the modulating Markov process, called rapid switching. We establish diffusion approximations, obtained by application of (semi)martingale central limit theorems. Depending on the specific circumstances, different approximations are found.

Weak convergence of Markov-modulated random sequences

Stochastics ◽  
2010 ◽  
Vol 82 (6) ◽  
pp. 521-552 ◽  
Author(s):  
Son Luu Nguyen ◽  
G. Yin
Keyword(s):  
Weak Convergence ◽  
Random Sequences ◽  
Markov Modulated

Approximation of periodic queues

1987 ◽  
Vol 19 (03) ◽  
pp. 691-707 ◽  
Author(s):  
Tomasz Rolski
Keyword(s):  
Weak Convergence ◽  
Time Of Day ◽  
Uniform Integrability ◽  
Queue Size ◽  
Approximation Theorems ◽  
Mean Delay ◽  
Periodic Queues ◽  
Poisson Arrivals ◽  
Markov Modulated

In this paper we demonstrate how some characteristics of queues with the periodic Poisson arrivals can be approximated by the respective characteristics in queues with Markov modulated input. These Markov modulated queues were recently studied by Regterschot and de Smit (1984). The approximation theorems are given in terms of the weak convergence of some characteristics and their uniform integrability. The approximations are applicable for the following characteristics: mean workload, mean workload at the time of day, mean delay, mean queue size.

Weak convergence of diffusion processes on Wiener space

2007 ◽  
Vol 140 (1-2) ◽  
pp. 1-17 ◽  
Author(s):  
Alexander V. Kolesnikov
Keyword(s):  
Weak Convergence ◽  
Diffusion Processes ◽  
Wiener Space

Approximation of periodic queues

1987 ◽  
Vol 19 (3) ◽  
pp. 691-707 ◽  
Author(s):  
Tomasz Rolski
Keyword(s):  
Weak Convergence ◽  
Time Of Day ◽  
Uniform Integrability ◽  
Queue Size ◽  
Approximation Theorems ◽  
Mean Delay ◽  
Periodic Queues ◽  
Poisson Arrivals ◽  
Markov Modulated

In this paper we demonstrate how some characteristics of queues with the periodic Poisson arrivals can be approximated by the respective characteristics in queues with Markov modulated input. These Markov modulated queues were recently studied by Regterschot and de Smit (1984). The approximation theorems are given in terms of the weak convergence of some characteristics and their uniform integrability. The approximations are applicable for the following characteristics: mean workload, mean workload at the time of day, mean delay, mean queue size.

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