的意思 homogeneous Markov chain

1. A homogeneous Markov chain is a stochastic process where the transition probabilities do not change over time.
一个同质马尔可夫链是一个随机过程，其中转移概率随时间不变。

2. In a homogeneous Markov chain, the future state of the system only depends on the current state and not on the history of the system.
在同质马尔可夫链中，系统未来状态仅取决于当前状态，而不取决于系统的历史。

3. The transition matrix of a homogeneous Markov chain remains constant over time.
同质马尔可夫链的转移矩阵随时间保持不变。

4. One common application of homogeneous Markov chains is in modeling the behavior of a system with a finite number of states.
同质马尔可夫链的一个常见应用是模拟具有有限状态数的系统的行为。

5. The steady-state distribution of a homogeneous Markov chain can be found by solving a set of linear equations.
同质马尔可夫链的稳态分布可以通过解一组线性方程来找到。

6. Understanding the properties of a homogeneous Markov chain is essential for analyzing the long-term behavior of a system.
理解同质马尔可夫链的属性对于分析系统的长期行为至关重要。