Eksempler på brug af Markov processes på Engelsk og deres oversættelser til Dansk
{-}
-
Colloquial
-
Official
-
Medicine
-
Financial
-
Ecclesiastic
-
Official/political
-
Computer
This work on Markov processes is described in and is introduced as follows.
Following Kolmogorov, Feller, Doob, and Ito,Dynkin opened a new chapter in the theory of Markov processes.
Efter Kolmogorov, FELLER, Doob, og Ito,Dynkin åbnet et nyt kapitel i teorien for Markov processer.He transformed the relation between Markov processes and partial differential equations.
Han omdannes forholdet mellem Markov processer og partielle differentialligninger.On Markov processes it has been carried out mostly in the United States by Doob, T E Harris and the reviewer.
På Markov processer det har været foretaget primært i USA ved Doob, TE Harris og reviewer.He generalised Lyapunov 's conditions for the central limit theorem, studied generalisations of the law of large numbers,worked on Markov processes and stochastic processes. .
Han generelle Lyapunov's betingelser for den centrale grænse sætning, studeret generaliseringer af de store tals lov,arbejdet på Markov processer og stokastiske He wrote on the theory of Markov processes and published an important series of articles on Markov transition probabilities which we gave details of above.
Han skrev om teorien om Markov processer og offentliggjort en lang række artikler om There Aleksandrov worked on the topology book which he co-authored with Hopf,while Kolmogorov worked on Markov processes with continuous states and continuous time.
Der Aleksandrov arbejdet på topologi bog, som han co-forfattet med Hopf, mensKolmogorov arbejdet på Markov processer med løbende stater og kontinuerlig tid.This work on Markov processes is described in and is introduced as follows: Following Kolmogorov, Feller, Doob, and Ito, Dynkin opened a new chapter in the theory of Markov processes.
Dette arbejde på Markov processer er beskrevet i og er indført som følger: Efter Kolmogorov, FELLER, Doob, og Ito, Dynkin åbnet et nyt kapitel i teorien for Markov processer.His work from this period is contained in two major books Foundations of the Theory of Markov Processes(1959) and Markov Processes(1963) which have become classics of probability theory.
Hans arbejde fra denne periode er indeholdt i to store bøger grundlaget for teorien om Markov Processer(1959) og Markov Processer(1963), der er blevet klassikere af sandsynlighedsteorien.A class of measure-valued Markov processes[which] can be used to give probabilistic solutions to certain nonlinear PDE's in a way which is analogous to the classical solution of the Dirichlet problem by means of Brownian motion.
En klasse af måle-værdiansættes Markov processer[der] kan bruges til at give probabilistiske løsninger på nogle bratte PDE's på en måde, der er analog med den klassiske løsning af Dirichlet problemet ved hjælp af Brownian motion.In 1960 Ito visited the Tata Institute in Bombay, India,where he gave a series of lectures surveying his own work and that of other on Markov processes, Levy processes, Brownian motion and linear diffusion.
I 1960 Ito besøgte Tata Institute i Bombay, Indien,hvor han gav en række foredrag surveying hans eget arbejde, og at andre på Markov processer, Levy There Aleksandrov worked on the topology book which he co-authored with Hopf,while Kolmogorov worked on Markov processes with continuous states and continuous time. Kolmogorov's results from his work by the Lake were published in 1931 and mark the beginning of diffusion theory.
Der Aleksandrov arbejdet på topologi bog, som han co-forfattet med Hopf, mensKolmogorov arbejdet på Markov processer med løbende stater og kontinuerlig tid. Kolmogorov's resultater fra hans arbejde ved søen blev offentliggjort i 1931 og markere begyndelsen af diffusion teori.Among the areas on which he has written papers we must mention: complex analysis, topological groups, fixed point theorems, Banach spaces andHilbert spaces, Markov processes, measure theory, flows, Brownian motion, and ergodic theory.
Blandt de områder, som han har skrevet papirer skal vi nævne: kompleks analyse, topologiske grupper, faste punkt teoremer,Banachrum og Hilbertrum, Markov processer, måle teori, strømme, Brownian motion, og ergodic teori.In the last few years Dynkin has obtained exciting results in the theory of"superprocesses"… a class of measure-valued Markov processes[which] can be used to give probabilistic solutions to certain nonlinear PDE's in a way which is analogous to the classical solution of the Dirichlet problem by means of Brownian motion.
I de sidste par år Dynkin har opnået spændende resultater i teorien om"superprocesses"… en klasse af måle-værdiansættes Markov processer[der] kan bruges til at give probabilistiske løsninger på nogle bratte PDE's på en måde, der er analog med den klassiske løsning af Dirichlet problemet ved hjælp af Brownian motion.This book contained five chapters, the first providing an introduction, then the remaining ones studying processes with independent increments,stationary processes, Markov processes, and the theory of diffusion processes. .
Denne bog indeholdt fem kapitler, det første giver en introduktion, og derefter de øvrige studerer In his work on the theory of Markov chains and processes, his main field, we notice major contributions to: Markov chains with general state spaces,Jump Markov processes, the coupling method(innovation), and diffusions.
I sit arbejde på teorien om In his hands it became a remarkable relation between occupation times of a Markov process and a related Gaussian random field.
I hans hænder blev det en bemærkelsesværdig forbindelse mellem erhverv gange af en Markov proces og en tilhørende Gauss tilfældig område.He created the fundamental concept of a Markov process as a family of measures corresponding to various initial times and states and he defined time homogeneous processes in terms of the shift operators.
Han skabte det grundlæggende koncept for en Markov proces som en familie af foranstaltninger svarende til forskellige indledende gange og stater og han defineret tid ensartede In 1923 Norbert Wiener became the first to treat rigorously a continuous Markov process.
I 1923 Norbert Wiener blev den første til at behandle stringent en kontinuerlig Markov proces.After mentioning the highly significant paper Analytic methods in probability theory which Kolmogorov published in 1938 laying the foundations of the theory of Markov random processes, they continue to describe.
After mentioning the highly significant paper Analytic methods in probability theory which Kolmogorov published in 1938 laying the foundations of the theory of Markov random processes, they continue to describe:… his ideas in set-theoretic topology, approximation theory, the theory of turbulent flow, functional analysis, the foundations of geometry, and the history and methodology of mathematics.
Efter at nævne den meget betydelige papir analytiske metoder i sandsynlighedsteorien som Kolmogorov offentliggjort i 1938 om grundlaget for teorien om Markov tilfældige processer, de fortsætter med at beskrive:… hans idéer i set-theoretic topologi, tilnærmelse teorien, teorien om turbulent flow, funktionelle analyse af grundlaget for geometri og historie og metodologi for matematik.
