What is Kolmogorov: Definition and 18 Discussions

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf] (listen), 25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.

View More On Wikipedia.org
Recent contents Top users
  1. Killtech

    I Bell vs Kolmogorov: Unravelling Probability Theory Limits

    For some reason on this forums here I found some weird opinions that Bell's inequality were somehow disqualifying classical probability theory in general rather then showing merely the limits of locality. I do no understand where that misunderstanding comes from, so I decided to find out. Let's...
  2. Killtech

    I Quantum physics vs Probability theory

    Because I do have a background in the latter it was originally very difficult for me to understand some aspects of QP (quantum physics) when I initially learned it. More specifically whenever probabilities were involved I couldn’t really make full sense of it while I never had any problems...
  3. F

    A Understanding Kolmogorov-Smirnov Test Results for Random Number Generators

    Hi all, I have some doubts regarding the Kolmogorov test: I made a simple c++ program generating two samples of random numbers following a Landau distribution (I used the "hit and miss" method). I made the Kolmogorov test, in order to check the randomness of the generator, but I'm having some...
  4. ATY

    Structure function in turbulence

    Hey guys, I need your help. I have to write a homework and we are actually looking at structure functions (Kolmogorov 41 and so on), but I have no clue what it does. So I have formulas, but I do not understand what a structure function is. Is it something in the "real world" or is it just a way...
  5. zrek

    I What "language" means in Kolmogorov complexity?

    Please help me to understand the answer I found on mathoverflow. The question was: "Do all uncountable sets contain elements with infinite Kolmogorov complexity?" The reasoning is clear for me, but I'd like to understand every word of the answer, which is the following: "...given a language...
  6. P

    Kolmogorov Entropy: Intuitive Understanding & Relation to Shannon Entropy

    Dear all, I'm trying to have an intuition of what Kolmogorov Entropy for a dynamical system means. In particular, 1. what is Kolmogorov Entropy trying to quantify? (what are the units of KS Entropy, is it bits or bits/seconds). 2. What is the relation of KS entropy to Shannon Entropy? 3. In...
  7. S

    Chapman Kolmogorov Th. - generality?

    Does the Chapman - Kolmogorov equation hold for an arbitrary stochastic process? The current wikipedia article on "Stochastic process" ( https://en.wikipedia.org/wiki/Stochastic_process ) seems to say that the Chapman-Kolmogorov equation is not valid for an arbitrary stochastic process. I...
  8. Fooality

    Help with Kolmogorov Complexity proof

    Hey, has anyone here done Kolmogorov complexity? I hadn't, and I was just reading the Wikipedia page to start learning it. The core concept makes sense: The Kolmogorov complexity for a a string s, K(s) is equivalent to the length of a program that generates that string (It can be any math...
  9. C

    Can the Kolmogorov definition of the conditional probability be proven

    It seems weird that such a relatively complex concept is simply given as a definition in most textbooks and then dismissed for further explanation other than using it intact or as a basis for further proofs.
  10. J

    Steady State Solution of Forward Kolmogorov Equation

    Essentially, this looks like a differential equation problem but being rusty on differential equations I am a little stuck. Homework Statement Consider the following SDE d\sigma = a(\sigma,t)dt + b(\sigma,t)dW The Forward Equation (FKE) is given by \frac{\partial p}{\partial t} =...
  11. J

    Kolmogorov smirnov in r - cannot compute correct p-values with ties

    Hi, I'm trying to use the kolmogorov smirnov test in in R to compare one distribution with another. I'm getting the following error: cannot compute correct p-values with ties I think this is because the dataset that I am using has in the first instance around 2000 values, and the second...
  12. N

    K41 Kolmogorov scaling relation and structure functions (turbulence)

    Hi there. I am having trouble interpreting the Kolmogorov K41 scaling relation for homogeneous and isotropic turbulence: S_{p}(l) = <\delta u(l)^{p}> = <|u(r+l) - u(r)|^{p}> \propto (\epsilon l)^{p/3} where l is the length of displacement between two points under consideration in the...
  13. Z

    Kolmogorov & Fomin's Elements of Theory: Real Analysis or Lebesque?

    I'm looking for a Real Analysis book to start with, besides Spivak. On Amazon, one of the reviewers said it was good as a subsequent book for learning Functional Analysis/Lebesque Integration, while another said it was a good introduction to Real Analysis. For those of you that have read it...
  14. D

    Solution of the Kolmogorov forward equation for a linear process

    Consider the 1-D linear system governed by: "dx/dt = a*x(t) + n(t)" where "a" is a scalar and: x(t) = system state n(t) ~ N(0, sigma^2) **************************** We can write Ito's stochastic differential equation of the previous process as: "dx = a*x*dt + 1/2*sigma^2*dW_t"...
  15. S

    Definition of a Kolmogorov Space

    Homework Statement Can a T_{0} topological space be created from the indiscrete topology of a set with only one element?
  16. D

    What are the differences between Blum and Kolmogorov complexities?

    Are they equivalent in some sense?
  17. S

    Kolmogorov complexity of SAT

    I'm not entirely clear on the concept of kolmogorov complexity. Does it mean that the a certain string is complex if there is no combinatorial (not sequential) circuit which outputs that string or does it mean that a certain string is complex if there is no program which can output that string...
  18. T

    Are Strings Kolmogorov-Random Actually Random?

    Are strings that are Kolmogorov-random actually random in the usual sense? An incompressible string probably won't contain this post anywhere in it, but a random one can.
Back
Top