escape probability造句

• In this dissertation , we firstly prove that any dirichlet problem is indeed equal to a voltages problem of networks . we give five solutions to dirichlet problem in two dimensions ; among these five solutions , we prove that the iteration solution and the solution of relaxations are exponential convergence , then we estimate their respective convergence rates ; secondly , we discuss random walks on general networks , prove that there is an one to one correspondence between networks and reversible ergodic markov chains ; thirdly , we give probabilistic interpretation of voltages for general networks : when a unit voltage is applied between a and b , making va = 1 and vb = 0 , the voltage vx at any point x represents the probability that a walker starting from x will return to a before reaching b ; furthermore , we study the relationship between effective resistance and escape probability : starting at a , the probability that the walk reaches b before returning to a is the ratio of the effective conductance and the total conductance
  本文证明了任何边值的dirichlet问题都可转化为求解电路电压的问题：给出了计算平面格点上dirichlet问题的5种方法：证明了迭代法和松驰法都是指数收敛的，并分别给出收敛速度的估计；讨论了一般电路上的随机徘徊，验证了电路与可逆的遍历markov链是一一对应的；给出了电路电压的概率解释：当把1伏电压加于a ， b两端，使得v _ a = 1 ， v _ b = 0时，则x点的电压v _ x表示对应的markov链中，从x出发，到达b之前到达a的概率；进一步地，给出了逃离概率与有效电阻之间的关系：从a出发，在到达b之前到达a的概率为有效传导率与通过a的总传导率之比。