random walk problem 中文意思是什麼
random walk problem
解釋
隨機走動問題-
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
本文證明了任何邊值的dirichlet問題都可轉化為求解電路電壓的問題：給出了計算平面格點上dirichlet問題的5種方法：證明了迭代法和松馳法都是指數收斂的，並分別給出收斂速度的估計；討論了一般電路上的隨機徘徊，驗證了電路與可逆的遍歷markov鏈是一一對應的；給出了電路電壓的概率解釋：當把1伏電壓加於a ， b兩端，使得v _ a = 1 ， v _ b = 0時，則x點的電壓v _ x表示對應的markov鏈中，從x出發，到達b之前到達a的概率；進一步地，給出了逃離概率與有效電阻之間的關系：從a出發，在到達b之前到達a的概率為有效傳導率與通過a的總傳導率之比。 -
Problem set 2 : continuum approximations of non - stationary random walks, random walk in a harmonic well, steps with fat tails, saddle - point asymptotics
問題2 ：非穩定型隨機漫步的連續極限，具調合井的隨機漫步，具備巨大尾部的漫步，鞍點近似解。 -
Problem set 3 : asymptotics of percentile order statistics, non - reversing random walk, self - trapping random walk, self - avoiding random walk
問題3 ：有序統計百分數的近似、非可逆隨機漫步、自已誘捕隨機漫步、自已避免隨機漫步。 -
In this paper, by using monte carlo method with irregular grid random walk in time - space domain the problem of mass concrete transient temperature field was solved
摘要利用求偏微分方程的蒙特卡羅演算法，通過在時空域中不規則網格隨機游動來求解大體積混凝土不穩定溫度場。
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