……有时在边缘问题上术语定义不清。语言干净、逻辑清晰、所有术语都定义并解释得明明白白，而且进阶内容充实的一本书是（带点 TeX 标记）：Erhan \c Cinlar, {\it Introduction to Stochastic Processes,\/} ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.\ \ 作者在普林斯顿任教多年，水平极高。当年我一边读研一边在一家公司做……
…undefined terminology sometimes about peripheral issues. Clean, logical, all terms well defined and explained, with plenty of advanced content, is in (with some markup using TeX) Erhan \c Cinlar, {\it Introduction to Stochastic Processes,\/} ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.\ \ The author was long at Princeton. He is a high quality guy. As I was working my way through grad school in a company working on…
……红蓝方的战备存量下降过程，就像一个从属于 Poisson 过程的多维、连续时间、离散状态空间（状态空间极大）的 Markov 过程（想找个好的入门，可以看看 E. Cinlar 的《随机过程引论》Introduction to Stochastic Processes）。因此，只要给定了速度、半径以及一对一红蓝交战时的结果——一方阵亡、另一方阵亡、同归于尽、或者都存活——所需的数据就全齐了。有了这些数据，我们就能做一些预测……
…the Red-Blue inventory declines like a multi-dimensional, continuous time, discrete state space (huge state space) Markov process subordinated to a Poisson process (for a good start, see the E. Cinlar Introduction to Stochastic Processes). So, given the speeds, radii, and what happens -- one dies, other dies, both die, neither die -- one on one, Red-Blue encounters, have all the data needed. Now with that data, we can make some predictions.…
……真正起作用的地方。”Keilson 虽然觉得“gnat's ass（小题大做）”这种糙话有点冒犯，但他喜欢其中的数学，并认可了我为美国海军做的研究。那个问题和答案值得铭记在心。更多内容可以参考比如 Erhan Çinlar 的《随机过程引论》（Introduction to Stochastic Processes, ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975）。关于为什么到达时间服从指数分布以及为什么会产生 Poisson 过程，Çinlar 给出了一套简洁、直观又实用的公理化……
…the action is.". Keilson was offended by "gnat's ass" but liked the math and approved my work for the US Navy. That question and answer are good to keep in mind. There is more in, say, Erhan Çinlar, Introduction to Stochastic Processes, ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975. For why the arrival times have exponential distribution and why we get a Poisson process, Çinlar has a nice simple, intuitive, useful axiomatic…
…standard work in such Markov processes to say how fast the concentrations reach the 'absorbing' states of 0% or 100%. The literature on Markov processes is enormous. For a start, consider: Erhan Çinlar, 'Introduction to Stochastic Processes', ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.
……独立性来源于基于测度论和 Radon-Nikodym 定理的概率论（Rudin 的《实分析与复分析》Real and Complex Analysis 中收录了冯·诺依曼的新颖证明），但更易读的入门可以看 Erhan Çınlar 的《随机过程引论》（Introduction to Stochastic Processes）。在 Poisson 过程中，到下一次事件发生的时间具有 Poisson 分布，因此经过简单的微积分推导，它就是一个 Markov 过程。比如，从现在起直到一个氢分子……
…independent is from probability theory based on measure theory and the Radon-Nikodym theorem (with von Neumann's novel proof in Rudin, Real and Complex Analysis), but an easier introduction is in Erhan Çınlar, Introduction to Stochastic Processes. In a Poisson process the time until the next event has the Poisson distribution and, thus, from a simple calculus manipulation, is a Markov process. E.g., time from now until a molecule of hydrogen…
……有时在边缘问题上术语定义不清。语言干净、逻辑清晰、所有术语都定义并解释得明明白白，而且进阶内容充实的一本书是（带点 TeX 标记）：Erhan \c Cinlar, {\it Introduction to Stochastic Processes,\/} ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.\ \ 作者在普林斯顿任教多年，水平极高。当年我一边读研一边在一家公司做……
…undefined terminology sometimes about peripheral issues. Clean, logical, all terms well defined and explained, with plenty of advanced content, is in (with some markup using TeX) Erhan \c Cinlar, {\it Introduction to Stochastic Processes,\/} ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.\ \ The author was long at Princeton. He is a high quality guy. As I was working my way through grad school in a company working on…
……红蓝方的战备存量下降过程，就像一个从属于 Poisson 过程的多维、连续时间、离散状态空间（状态空间极大）的 Markov 过程（想找个好的入门，可以看看 E. Cinlar 的《随机过程引论》Introduction to Stochastic Processes）。因此，只要给定了速度、半径以及一对一红蓝交战时的结果——一方阵亡、另一方阵亡、同归于尽、或者都存活——所需的数据就全齐了。有了这些数据，我们就能做一些预测……
…the Red-Blue inventory declines like a multi-dimensional, continuous time, discrete state space (huge state space) Markov process subordinated to a Poisson process (for a good start, see the E. Cinlar Introduction to Stochastic Processes). So, given the speeds, radii, and what happens -- one dies, other dies, both die, neither die -- one on one, Red-Blue encounters, have all the data needed. Now with that data, we can make some predictions.…
……真正起作用的地方。”Keilson 虽然觉得“gnat's ass（小题大做）”这种糙话有点冒犯，但他喜欢其中的数学，并认可了我为美国海军做的研究。那个问题和答案值得铭记在心。更多内容可以参考比如 Erhan Çinlar 的《随机过程引论》（Introduction to Stochastic Processes, ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975）。关于为什么到达时间服从指数分布以及为什么会产生 Poisson 过程，Çinlar 给出了一套简洁、直观又实用的公理化……
…the action is.". Keilson was offended by "gnat's ass" but liked the math and approved my work for the US Navy. That question and answer are good to keep in mind. There is more in, say, Erhan Çinlar, Introduction to Stochastic Processes, ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975. For why the arrival times have exponential distribution and why we get a Poisson process, Çinlar has a nice simple, intuitive, useful axiomatic…
……关于这类 Markov 过程的经典研究，足以说明浓度以多快的速度达到 0% 或 100% 的“吸收”态（absorbing states）。关于 Markov 过程的文献汗牛充栋。作为起步，可以参考：Erhan Çinlar 的《随机过程引论》（Introduction to Stochastic Processes, ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975）。
…standard work in such Markov processes to say how fast the concentrations reach the 'absorbing' states of 0% or 100%. The literature on Markov processes is enormous. For a start, consider: Erhan Çinlar, 'Introduction to Stochastic Processes', ISBN 0-13-498089-1, Prentice-Hall, Englewood Cliffs, NJ, 1975.
E. Cinlar 的《随机过程引论》（Introduction to Stochastic Processes），涵盖了极限定理和连续时间。
E. Cinlar, Introduction to Stochastic Processes Covers limit theorems and continuous time.
……独立性来源于基于测度论和 Radon-Nikodym 定理的概率论（Rudin 的《实分析与复分析》Real and Complex Analysis 中收录了冯·诺依曼的新颖证明），但更易读的入门可以看 Erhan Çınlar 的《随机过程引论》（Introduction to Stochastic Processes）。在 Poisson 过程中，到下一次事件发生的时间具有 Poisson 分布，因此经过简单的微积分推导，它就是一个 Markov 过程。比如，从现在起直到一个氢分子……
…independent is from probability theory based on measure theory and the Radon-Nikodym theorem (with von Neumann's novel proof in Rudin, Real and Complex Analysis), but an easier introduction is in Erhan Çınlar, Introduction to Stochastic Processes. In a Poisson process the time until the next event has the Poisson distribution and, thus, from a simple calculus manipulation, is a Markov process. E.g., time from now until a molecule of hydrogen…