stochastischer Prozess auf
English translation: stochastic process defined for
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| 21:07 Oct 15, 2018 |
| German to English translations [PRO] Science - Mathematics & Statistics / Stochastic processes | |||||||
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|  Selected response from: Johanna Timm, PhD Canada Local time: 16:39 | ||||||
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| 4 +1 | stochastic process over [index set] |
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| 3 | stochastic process represented by |
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| 3 | stochastic process defined for |
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Answers
2 hrs confidence: 
stochastic process represented by Explanation: A stochastic process is a random process evolving with time. More specifically, in probability theory, a stochastic process is a time sequence representing the evolution of some system represented by a variable whose change is subject to a random variation. T c R^1 in your case |
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3 hrs confidence:
stochastic process defined for Explanation: The TLF is a stochastic process defined for independent variables. And real-world financial data often present autocorrelations. https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0404/0... Let X(t) be a stochastic process defined for t E (a, b). Suppose that for all (t, t + h) belonging to (a, b) it results that : where g(h) and q(h) are even, non decreasing ... www.numdam.org/article/AIHPB_1982__18_4_367_0.pdf Attainable discrete-time stochastic process: A discrete- time stochastic process defined for (only) a (finite) dis-crete time range bobweigel.net/csi763/.../Bingham_1967_Modern_Power_Spectrum_Techniques.pdf |
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11 hrs confidence: peer agreement (net): +1
peer agreement (net): +1stochastic process over [index set] Explanation: - a stochastic process over T c R^1 - a function defined over T x Omega https://link.springer.com/chapter/10.1007/978-3-642-39632-8_... Ein stochastischer Prozeß \(\mathcal{X}\) über einem Wahrscheinlichkeitsraum \([\Omega,\mathcal{A}_{\sigma},\mathbb{P}]\) ist in erster Näherung aufzufassen als eine Familie {ξ t : t ∈ T} von Zufallsgrößen ξ t : Ω → X (T eine geeignete Indexmenge, X ein metrischer Raum). https://link.springer.com/referenceworkentry/10.1007/978-3-6... In other words, a primary interpretation of a stochastic process X is as a collection of random variables, and as such, notations like (X t) t ∈ T are used to refer to X, that is X t (ω) = X(t, ω), for all (t, ω) ∈ T ×Ω. https://www.di.ens.fr/~keeler/TechnicalReports/StochasticPro... A stochastic or random process is a collection of random variables that is indexed by or depends on some mathematical set [120, page 7][66, page 1]. More formally, a stochastic process is defined as a collection of random variables defined on a common probability space ( ;F; ; P), where is a sample space, F is a - algebra, and P is a probability measure, and the random variables, indexed by some set T -------------------------------------------------- Note added at 7 days (2018-10-23 06:57:37 GMT) Post-grading -------------------------------------------------- My instinct of 'over' in both of your examples stems from 4 university courses involving linear algebra, quantum mechanics or computational chemistry. It was confirmed by 2 bi/trilingual people with a true passion for mathematics. If you were unsure after searching "stochastic process defined over", "function over" or "over set T", you could have asked for more help. 'Defined for' is nonsense in your given text. Should look familiar: https://ttu-ir.tdl.org/ttu-ir/bitstream/handle/2346/11489/31... JACKKNIFING STOCHASTIC PROCESSES USING THE SECOND ORDER J-ESTIMATOR by JASPER EMMETT ADAMS, JR., B.S., M.S. A DISSERTATION IN MATHEMATICS Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY ... Let {G(t)|t∈S} be a stochastic process defined over a continuous index set S whose probability law depends on θ for every t belonging to S. |
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