Introduction to Stochastic Processes
by Erhan Cinlar · first published 2013
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…Rudin, Functional Analysis Leo Breiman, Probability Kai Lai Chung, A Course in Probability Theory, Second Edition Jacques Neveu, Mathematical Foundations of the Calculus of Probability Erhan Cinlar, Introduction to Stochastic Processes J. L. Doob, Stochastic Processes I. I. Gihman and A. V. Skorohod, The Theory of Stochastic Processes I, II Donald E. Knuth, The TeX book Donald E. Knuth, The Art of Computer Programming, Second Edition…
on “Ask HN: Older textbooks/papers you consider classics still worth studying today?” ↗…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…
on “Forecasting s-curves is hard” ↗…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.
on “New Statistical Law Discovered” ↗The one I'm enjoying right now is Introduction to Stochastic Processes by Erhan Cinlar.
on “Ask HN: Math books that made you significantly better at math?” ↗…are stationary and independent, then the inter-arrival times are independent and have the same exponential distribution. Good details are early in the chapter on Poisson processes in Erhan Cinlar, 'Introduction to Stochastic Processes', ISBN 0-13-498089-1, Prentice-Hall. Downey's book places a lot of emphasis on distributions, e.g., Weibull, and descriptions, e.g., skewness. So an implication is, given some data, we should try to…
on “Think Stats, using python to learn stats ” ↗…or acoustical signals and noise. There are commonly interested in power spectral estimation, digital filtering, maybe Wiener filtering, the fast Fourier transform, etc. or (2) what is in, say, Cinlar, Introduction to Stochastic Processes. In Cinlar, for the continuous time case, get a good introduction to the Poisson process (the vanilla arrival process, e.g., like clicks at a Geiger counter, new sessions at a Web site, and much more).…
on “Foundations of probability theory” ↗It's all much easier than that: It's just the Poisson process, e.g., with a nice chapter in E. Cinlar, Introduction to Stochastic Processes. Buses come as arrivals. So bus arrivals are a stochastic arrival process where stochastic just means varying randomly over time where, really, the randomly doesn't mean anything, includes deterministic…
on “The Waiting Time Paradox, Or, Why Is My Bus Always Late?” ↗…is the Poisson stochastic arrival (get arrivals at discrete points in time) process. There are two amazing, powerful, useful, non-obvious biggie points: (1)Axiomatic Derivation As in Erhan Çinlar, 'Introduction to Stochastic Processes', ISBN 0-13-498089-1. an arrival process with stationary (distribution not changing over time) independent (of all past history of the process) increments (arrivals) is necessarily a Poisson process.…
on “Some Useful Probability Facts for Systems Programming” ↗…process encounter rate work from the B. O. Koopman, OEG-56 Search and Screening and some of the rest was on continuous time, discrete state space Markov processes subordinated to a Poisson process from Erhan Çinlar, Introduction to Stochastic Processes, ISBN 0-13-498089-1. from which I'd recently had a course. (C) For my startup, I wanted a good way to handle user session state. So, I wrote a session state server. Sure, Redis could have been used…
on “Y Combinator's Paul Buchheit:The Surprising Learned from 200+ Startups (2016)” ↗…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.…
on “Foundations Machine Learning” ↗