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| | <math>Q'_{kl}=\sum_{j\in B_l}Q^{ij},i\in B_k</math> | | <math>Q'_{kl}=\sum_{j\in B_l}Q^{ij},i\in B_k</math> |
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| − | 强成块性确保了区块内状态的不可区分性,粗粒化过程严格保持瞬态与稳态分布。<ref name=":9">Lumpability for Uncertain Continuous-Time Markov Chains
| + | 强成块性确保了区块内状态的不可区分性,粗粒化过程严格保持瞬态与稳态分布<ref name=":9">Luca Cardelli and Radu Grosu and Kim G. Larsen and Mirco Tribastone and Max Tschaikowski and Andrea Vandin. Lumpability for Uncertain Continuous-Time Markov Chains. QEST, 2021, 391-409.</ref>。 |
| − | .Springer Science & Business Media, 1999, 53-156.</ref>
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| | + | ====时间尺度分解==== |
| | + | 对于有快慢分离特性的系统,快变量可很快达到准稳态,慢变量主导宏观动力学。设快变量状态集<math>S_f</math>和慢变量状态集<math>S_s</math>,粗粒化后的转移速率矩阵<math>Q'</math>的元素计算为: |
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| − | @inproceedings{DBLP:conf/qest/CardelliGLTTV21,
| + | <math>Q'_{kl}=\frac{\sum_{i\in B_k}\sum_{j\in B_l}\pi_i^{B_k}Q_{ij}}{\sum_{I\in B_k}\pi_i^{B_k}}</math> |
| − | author={Luca Cardelli and Radu Grosu and Kim G. Larsen and Mirco Tribastone and Max Tschaikowski and Andrea Vandin},
| + | |
| − | title={Lumpability for Uncertain Continuous-Time Markov Chains},
| + | 其中<math>\pi_i^{B_k}</math>为区块<math>B_k</math>内状态的准稳态分布,该方法在生物化学网络和通信协议中广泛应用<ref name=":10">Daria Stepanova, Helen M. Byrne, Philip K. Maini, and Tomás Alarcón. A Method to Coarse-Grain Multiagent Stochastic Systems with Regions of Multistability. Multiscale Model. Simul. 2022, 20(1):404-432.</ref>。 |
| − | year={2021},
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| − | cdate={1609459200000},
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| − | pages={391-409},
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| − | url={https://doi.org/10.1007/978-3-030-85172-9_21},
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| − | booktitle={QEST},
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| − | crossref={conf/qest/2021}
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| − | }
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| | ==参考文献== | | ==参考文献== |
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| | <references /> | | <references /> |