See stochastic process in All languages combined, or Wiktionary
Download JSON data for stochastic process meaning in English (5.5kB)
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{
"ref": "1994, Andrzej Lasota, Michael C. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, 2nd edition, Springer, page 254",
"text": "A stochastic process #x5C;#x7B;#x5C;zeta#x5F;t#x5C;#x7D; is a family of random variables that depends on a parameter t, usually called time.[…]Two important properties stochastic processes may have are given in the following definition.",
"type": "quotation"
},
{
"ref": "2009, Charlotte Werndl, “Deterministic Versus Indeterministic Descriptios: Not That Different After All”, in Alexander Hieke, Hannes Leitgeb, editors, Reduction - Abstraction - Analysis, page 71",
"text": "Hence even Bernoulli processes, often regarded as the most random stochastic processes, are simulated by deterministic systems in science when observed with specific observation functions. But then any attempt to separate such deterministic systems from the deterministic systems needed to simulate the stochastic processes in science must fail. The philosophical implication of this result is that the above guess is wrong, viz. the deterministic systems which simulate the stochastic processes in science include deterministic systems in science. This indicates that from a predictive viewpoint, stochastic processes and deterministic systems are very similar.",
"type": "quotation"
},
{
"ref": "2014, Pierre Brémaud, Fourier Analysis and Stochastic Processes, Springer, page xi",
"text": "A unified treatment of all the aspects of Fourier theory relevant to the Fourier analysis of stochastic processes is not only unavoidable, but also intellectually satisfying, and in fact time-saving.",
"type": "quotation"
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],
"glosses": [
"A function that maps elements of an index set to elements of a collection of random variables; historically, a collection of random variables indexed by a set of numbers usually regarded as points in time."
],
"id": "en-stochastic_process-en-noun-uB1jAGyC",
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"raw_glosses": [
"(mathematics, probability theory) A function that maps elements of an index set to elements of a collection of random variables; historically, a collection of random variables indexed by a set of numbers usually regarded as points in time."
],
"related": [
{
"word": "sample path"
}
],
"synonyms": [
{
"sense": "function mapping to a random variable",
"word": "probabilistic process"
},
{
"sense": "function mapping to a random variable",
"word": "probability process"
},
{
"sense": "function mapping to a random variable",
"word": "random process"
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"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "a function mapping to set of random variables",
"word": "隨機過程"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "suíjī guòchéng",
"sense": "a function mapping to set of random variables",
"word": "随机过程"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "a function mapping to set of random variables",
"word": "stokastinen prosessi"
},
{
"code": "de",
"lang": "German",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "stochastischer Prozess"
},
{
"code": "de",
"lang": "German",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "Zufallsprozeß"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "tahalích stochásti",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "תהליך סטוכסטי"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "tahalích akra'í",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "תהליך אקראי"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "a function mapping to set of random variables",
"tags": [
"neuter"
],
"word": "slembiferli"
},
{
"code": "it",
"lang": "Italian",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "processo stocastico"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "kakuritsukatei",
"sense": "a function mapping to set of random variables",
"word": "確率過程"
},
{
"code": "pl",
"lang": "Polish",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "proces stochastyczny"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "a function mapping to set of random variables",
"tags": [
"neuter"
],
"word": "proces stocastic"
}
],
"wikipedia": [
"stochastic process"
]
}
],
"word": "stochastic process"
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{
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"ref": "1994, Andrzej Lasota, Michael C. Mackey, Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics, 2nd edition, Springer, page 254",
"text": "A stochastic process #x5C;#x7B;#x5C;zeta#x5F;t#x5C;#x7D; is a family of random variables that depends on a parameter t, usually called time.[…]Two important properties stochastic processes may have are given in the following definition.",
"type": "quotation"
},
{
"ref": "2009, Charlotte Werndl, “Deterministic Versus Indeterministic Descriptios: Not That Different After All”, in Alexander Hieke, Hannes Leitgeb, editors, Reduction - Abstraction - Analysis, page 71",
"text": "Hence even Bernoulli processes, often regarded as the most random stochastic processes, are simulated by deterministic systems in science when observed with specific observation functions. But then any attempt to separate such deterministic systems from the deterministic systems needed to simulate the stochastic processes in science must fail. The philosophical implication of this result is that the above guess is wrong, viz. the deterministic systems which simulate the stochastic processes in science include deterministic systems in science. This indicates that from a predictive viewpoint, stochastic processes and deterministic systems are very similar.",
"type": "quotation"
},
{
"ref": "2014, Pierre Brémaud, Fourier Analysis and Stochastic Processes, Springer, page xi",
"text": "A unified treatment of all the aspects of Fourier theory relevant to the Fourier analysis of stochastic processes is not only unavoidable, but also intellectually satisfying, and in fact time-saving.",
"type": "quotation"
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],
"glosses": [
"A function that maps elements of an index set to elements of a collection of random variables; historically, a collection of random variables indexed by a set of numbers usually regarded as points in time."
],
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"(mathematics, probability theory) A function that maps elements of an index set to elements of a collection of random variables; historically, a collection of random variables indexed by a set of numbers usually regarded as points in time."
],
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{
"sense": "function mapping to a random variable",
"word": "probabilistic process"
},
{
"sense": "function mapping to a random variable",
"word": "probability process"
},
{
"sense": "function mapping to a random variable",
"word": "random process"
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],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "a function mapping to set of random variables",
"word": "隨機過程"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "suíjī guòchéng",
"sense": "a function mapping to set of random variables",
"word": "随机过程"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "a function mapping to set of random variables",
"word": "stokastinen prosessi"
},
{
"code": "de",
"lang": "German",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "stochastischer Prozess"
},
{
"code": "de",
"lang": "German",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "Zufallsprozeß"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "tahalích stochásti",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "תהליך סטוכסטי"
},
{
"code": "he",
"lang": "Hebrew",
"roman": "tahalích akra'í",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
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"word": "תהליך אקראי"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "a function mapping to set of random variables",
"tags": [
"neuter"
],
"word": "slembiferli"
},
{
"code": "it",
"lang": "Italian",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "processo stocastico"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "kakuritsukatei",
"sense": "a function mapping to set of random variables",
"word": "確率過程"
},
{
"code": "pl",
"lang": "Polish",
"sense": "a function mapping to set of random variables",
"tags": [
"masculine"
],
"word": "proces stochastyczny"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "a function mapping to set of random variables",
"tags": [
"neuter"
],
"word": "proces stocastic"
}
],
"word": "stochastic process"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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