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21 relations: Andrey Kolmogorov, Birth, Brownian motion, Chapman–Kolmogorov equation, Diffusion, Fokker–Planck equation, Itô diffusion, Jump process, Kolmogorov backward equations (diffusion), Kolmogorov equations (Markov jump process), Kolmogorov forward equations, Markov chain, Master equation, Motoo Kimura, Natural science, Population growth, Population size, Probability, Probability theory, Stochastic process, William Feller.
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
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Birth
Birth is the act or process of bearing or bringing forth offspring.
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Brownian motion
Brownian motion or pedesis (from πήδησις "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid.
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Chapman–Kolmogorov equation
In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process.
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Diffusion
Diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules or atoms.
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Fokker–Planck equation
In statistical mechanics, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion.
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Itô diffusion
In mathematics — specifically, in stochastic analysis — an Itô diffusion is a solution to a specific type of stochastic differential equation.
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Jump process
A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.
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Kolmogorov backward equations (diffusion)
The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes.
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Kolmogorov equations (Markov jump process)
In the context of a continuous-time Markov process, the Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, are a pair of systems of differential equations that describe the time-evolution of the probability P(x,s;y,t), where x, y \in \Omega (the state space) and t > s are the final and initial time respectively.
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Kolmogorov forward equations
Kolmogorov forward equations may refer to.
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Markov chain
A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".
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Master equation
In physics, chemistry and related fields, master equations are used to describe the time evolution of a system that can be modelled as being in a probabilistic combination of states at any given time and the switching between states is determined by a transition rate matrix.
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Motoo Kimura
(November 13, 1924 – November 13, 1994) was a Japanese biologist best known for introducing the neutral theory of molecular evolution in 1968, in collaboration with Tomoko Ohta.
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Natural science
Natural science is a branch of science concerned with the description, prediction, and understanding of natural phenomena, based on empirical evidence from observation and experimentation.
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Population growth
In biology or human geography, population growth is the increase in the number of individuals in a population.
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Population size
In population genetics and population ecology, population size (usually denoted N) is the number of individual organisms in a population.
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Probability
Probability is the measure of the likelihood that an event will occur.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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William Feller
William "Vilim" Feller (July 7, 1906 – January 14, 1970), born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory.
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Forward equation, Kolmogorov Backward equation, Kolmogorov backward equation, Kolmogorov forward equation.
References
[1] https://en.wikipedia.org/wiki/Kolmogorov_equations
