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rdfs:label: 確率微分方程式 Équation différentielle stochastique معادلة تفاضلية تصادفية Ecuación diferencial estocástica 隨機微分方程 Equazione differenziale stocastica Stochastische Differentialgleichung Στοχαστική διαφορική εξίσωση Stochastic differential equation Стохастичне диференціальне рівняння Stokastisk differentialekvation Equação diferencial estocástica Стохастическое дифференциальное уравнение
rdfs:comment: A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes. are conjugate to stochastic differential equations. Une équation différentielle stochastique (EDS) est une généralisation de la notion d'équation différentielle prenant en compte un terme de bruit blanc. Les EDS permettent de modéliser des trajectoires aléatoires, tels des cours de bourse ou les mouvements de particules soumises à des phénomènes de diffusion. Elles permettent aussi de traiter théoriquement ou numériquement des problèmes issus de la théorie des équations aux dérivées partielles. Der Begriff der stochastischen Differentialgleichung (Abkürzung SDGL oder englisch SDE für stochastic differential equation) ist in der Mathematik eine Verallgemeinerung des Begriffs der gewöhnlichen Differentialgleichung auf stochastische Prozesse.Stochastische Differentialgleichungen werden in zahlreichen Anwendungen eingesetzt, um zeitabhängige Vorgänge zu modellieren, die neben deterministischen Einflüssen zusätzlich stochastischen Störfaktoren (Rauschen) ausgesetzt sind. Στοχαστική διαφορική εξίσωση λέγεται η διαφορική εξίσωση στην οποία ένας ή περισσότεροι όροι είναι στοχαστικές διαδικασίες, που σημαίνει ότι η λύση είναι και η ίδια στοχαστική διαδικασία.Για παράδειγμα η εξίσωση dXt=b(t,Xt)dt+σ(t,Xt)dWt όπου Wt μια m-διάστατη κίνηση Brown, αποτελεί μια στοχαστική διαφορική εξίσωση. Ο πρώτος όρος είναι ένας όρος τάσης και αποτελεί το ντετερμινιστικό μέρος της εξίσωσης και το δεύτερο άθροισμα αποτελεί το όρο διάχυσης και είναι μια στοχαστική διαδικασία.Μια στοχαστική διαφορική εξίσωση έχει λύση αν υπάρχει διαδικασία Ito Xt που την ικανοποιεί. En stokastisk differentialekvation är en differentialekvation där en eller flera av termerna är stokastiska processer. De används i modeller av diverse fenomen, exempelvis börskurser. Una equazione differenziale stocastica (abbreviato in EDS) (o stochastic differential equation, abbreviato in SDE ) è una equazione differenziale in cui uno o più termini sono processi stocastici, portando quindi ad una soluzione che è anch'essa un processo stocastico. Le EDS sono usate per modellare diversi fenomeni come la fluttuazione dei prezzi di azioni, o sistemi fisici soggetti a fluttuazioni termiche. Tipicamente, le EDS incorporano rumore bianco che può essere pensato come la derivata di un moto browniano (o meglio, di un processo di Wiener); ad ogni modo, vale menzionare che altri tipi di fluttuazioni casuali sono possibili, come i processi di salto. 確率微分方程式（かくりつびぶんほうていしき、英: Stochastic differential equation）とは、1つ以上の項が確率過程である微分方程式であって、その結果、解自身も確率過程となるものである。一般的に、確率微分方程式はブラウン運動（ウィーナー過程）から派生すると考えられる白色雑音を組み込むが、不連続過程の様な他の無作為変動を用いることも可能である。 المعادلة التفاضلية التصادفية (بالإنجليزية: Stochastic differential equation)‏ (SDE) هي معادلة تفاضلية يكون فيها واحد أو أكثر من الحدود عملية تصادفية، مما يؤدي إلى حل وهو أيضًا عملية تصادفية. تُستخدم "SDEs" لنمذجة ظواهر مختلفة مثل أسعار الأسهم غير المستقرة أو الأنظمة الفيزيائية الخاضعة للتقلبات الحرارية. عادةً ما تحتوي SDEs على متغير يمثل ضجيج أبيض عشوائي محسوب كمشتق من الحركة البراونية أو عملية فينر. ومع ذلك، هناك أنواع أخرى من السلوك العشوائي ممكنة، مثل عمليات القفز. المعادلات التفاضلية العشوائية مرتبطة بالمعادلات التفاضلية التصادفية. Una ecuación diferencial estocástica (EDE) es una ecuación diferencial en la cual uno o más de sus términos es un proceso estocástico y cuya solución es también un proceso estocástico. Las ecuaciones diferenciales estocásticas se utilizan para modelar diversos fenómenos como los precios de las acciones. Usualmente, las ecuaciones diferenciales estocásticas tienen ruido blanco que puede ser interpretado como la derivada del movimiento browniano o del proceso de Wiener. Sin embargo, debe mencionarse que otro tipo de fluctuaciones aleatorias son posibles como el . Este artigo discorre (apresenta e discute de forma simples e para um público leigo) sobre Equações Diferenciais Estocásticas, um novo grupo de equações usadas em modelagem, geralmente empregadas tanto quando não temos uma noção precisa do sistema que temos em mãos ou quando não temos meios para criar um modelo preciso (geralmente modelos assim são chamados de "caixa cinza"). 隨機微分方程（英語：SDE, stochastic differential equation），是微分方程的擴展。一般微分方程的對象為可導函數，並以其建立等式。然而，隨機過程函數本身的導數不可定義，所以一般解微分方程的概念不適用於隨機微分方程。隨機微分方程多用於對一些多样化现象进行建模，比如不停变动的股票价格，部分物理现象如等。隨機微分方程的概念最早以布朗運動的形式，由阿爾伯特·愛因斯坦在《热的分子运动论所要求的静液体中悬浮粒子的运动》論文中提出。这项研究隨後由保羅·朗之萬继续。此後伊藤清和完善了隨機微分方程的數學基礎，使得這門領域更加的科學嚴謹。一般而言，隨機微分方程的解是一隨機過程函數，但解方程需要先定義隨機過程函數的微分。最常見的定義為根據伊藤清所創，假設B為布朗運動，則對於某函數H，作以下定積分之定義：此稱為伊藤積分。伊藤式的隨機微分方程常用於在金融數學中。 Стохасти́чні диференціа́льні рівня́ння (СДР) — це диференціальні рівняння, в яких один або більше членів є стохастичним процесом, тому розв'язком СДР є випадковий (стохастичний) процес. Зазвичай, стохастичні диференціальні рівняння містять білий шум, який можна уявляти як диференціал від вінерівського процесу (іноді його ще називають Броунівським рухом), варто зазначити, що інші типи випадковості можуть мати місце в СДР, наприклад стрибкові процеси. Стохастическое дифференциальное уравнение (СДУ) — дифференциальное уравнение, в котором один член или более имеют стохастическую природу, то есть представляют собой стохастический (случайный) процесс. Таким образом, решения уравнения также оказываются стохастическими процессами. Наиболее известный и часто используемый пример СДУ — уравнение с членом, описывающим белый шум (который можно рассматривать как пример производной винеровского процесса). Однако существуют и другие типы случайных флуктуаций, например .
rdfs:seeAlso: dbr:Langevin_equation
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dbo:abstract: En stokastisk differentialekvation är en differentialekvation där en eller flera av termerna är stokastiska processer. De används i modeller av diverse fenomen, exempelvis börskurser. Este artigo discorre (apresenta e discute de forma simples e para um público leigo) sobre Equações Diferenciais Estocásticas, um novo grupo de equações usadas em modelagem, geralmente empregadas tanto quando não temos uma noção precisa do sistema que temos em mãos ou quando não temos meios para criar um modelo preciso (geralmente modelos assim são chamados de "caixa cinza"). As investigações de Einstein no movimento browniano institui um dos pontos mais supinos na longa reminiscência de averiguações na teoria cinética do calor, hoje asilada no meio acadêmico de forma visivelmente unânime, ou mesmo na estrada de Einstein no campo. Una ecuación diferencial estocástica (EDE) es una ecuación diferencial en la cual uno o más de sus términos es un proceso estocástico y cuya solución es también un proceso estocástico. Las ecuaciones diferenciales estocásticas se utilizan para modelar diversos fenómenos como los precios de las acciones. Usualmente, las ecuaciones diferenciales estocásticas tienen ruido blanco que puede ser interpretado como la derivada del movimiento browniano o del proceso de Wiener. Sin embargo, debe mencionarse que otro tipo de fluctuaciones aleatorias son posibles como el . Стохасти́чні диференціа́льні рівня́ння (СДР) — це диференціальні рівняння, в яких один або більше членів є стохастичним процесом, тому розв'язком СДР є випадковий (стохастичний) процес. Зазвичай, стохастичні диференціальні рівняння містять білий шум, який можна уявляти як диференціал від вінерівського процесу (іноді його ще називають Броунівським рухом), варто зазначити, що інші типи випадковості можуть мати місце в СДР, наприклад стрибкові процеси. 隨機微分方程（英語：SDE, stochastic differential equation），是微分方程的擴展。一般微分方程的對象為可導函數，並以其建立等式。然而，隨機過程函數本身的導數不可定義，所以一般解微分方程的概念不適用於隨機微分方程。隨機微分方程多用於對一些多样化现象进行建模，比如不停变动的股票价格，部分物理现象如等。隨機微分方程的概念最早以布朗運動的形式，由阿爾伯特·愛因斯坦在《热的分子运动论所要求的静液体中悬浮粒子的运动》論文中提出。这项研究隨後由保羅·朗之萬继续。此後伊藤清和完善了隨機微分方程的數學基礎，使得這門領域更加的科學嚴謹。一般而言，隨機微分方程的解是一隨機過程函數，但解方程需要先定義隨機過程函數的微分。最常見的定義為根據伊藤清所創，假設B為布朗運動，則對於某函數H，作以下定積分之定義：此稱為伊藤積分。伊藤式的隨機微分方程常用於在金融數學中。 Der Begriff der stochastischen Differentialgleichung (Abkürzung SDGL oder englisch SDE für stochastic differential equation) ist in der Mathematik eine Verallgemeinerung des Begriffs der gewöhnlichen Differentialgleichung auf stochastische Prozesse.Stochastische Differentialgleichungen werden in zahlreichen Anwendungen eingesetzt, um zeitabhängige Vorgänge zu modellieren, die neben deterministischen Einflüssen zusätzlich stochastischen Störfaktoren (Rauschen) ausgesetzt sind. Die mathematische Formulierung des Problems stellte die Mathematiker vor große Probleme, und so wurde die formale Theorie der stochastischen Differentialgleichungen erst in den 1940er Jahren durch den japanischen Mathematiker Itō Kiyoshi formuliert. Gemeinsam mit der stochastischen Integration begründet die Theorie der stochastischen Differentialgleichungen die stochastische Analysis. Una equazione differenziale stocastica (abbreviato in EDS) (o stochastic differential equation, abbreviato in SDE ) è una equazione differenziale in cui uno o più termini sono processi stocastici, portando quindi ad una soluzione che è anch'essa un processo stocastico. Le EDS sono usate per modellare diversi fenomeni come la fluttuazione dei prezzi di azioni, o sistemi fisici soggetti a fluttuazioni termiche. Tipicamente, le EDS incorporano rumore bianco che può essere pensato come la derivata di un moto browniano (o meglio, di un processo di Wiener); ad ogni modo, vale menzionare che altri tipi di fluttuazioni casuali sono possibili, come i processi di salto. A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes. are conjugate to stochastic differential equations. Une équation différentielle stochastique (EDS) est une généralisation de la notion d'équation différentielle prenant en compte un terme de bruit blanc. Les EDS permettent de modéliser des trajectoires aléatoires, tels des cours de bourse ou les mouvements de particules soumises à des phénomènes de diffusion. Elles permettent aussi de traiter théoriquement ou numériquement des problèmes issus de la théorie des équations aux dérivées partielles. Les domaines d'application des EDS sont vastes : physique, biologie, dynamique des populations, écologie, mathématiques financières, traitement du signal, théorie du contrôle… Стохастическое дифференциальное уравнение (СДУ) — дифференциальное уравнение, в котором один член или более имеют стохастическую природу, то есть представляют собой стохастический (случайный) процесс. Таким образом, решения уравнения также оказываются стохастическими процессами. Наиболее известный и часто используемый пример СДУ — уравнение с членом, описывающим белый шум (который можно рассматривать как пример производной винеровского процесса). Однако существуют и другие типы случайных флуктуаций, например . Στοχαστική διαφορική εξίσωση λέγεται η διαφορική εξίσωση στην οποία ένας ή περισσότεροι όροι είναι στοχαστικές διαδικασίες, που σημαίνει ότι η λύση είναι και η ίδια στοχαστική διαδικασία.Για παράδειγμα η εξίσωση dXt=b(t,Xt)dt+σ(t,Xt)dWt όπου Wt μια m-διάστατη κίνηση Brown, αποτελεί μια στοχαστική διαφορική εξίσωση. Ο πρώτος όρος είναι ένας όρος τάσης και αποτελεί το ντετερμινιστικό μέρος της εξίσωσης και το δεύτερο άθροισμα αποτελεί το όρο διάχυσης και είναι μια στοχαστική διαδικασία.Μια στοχαστική διαφορική εξίσωση έχει λύση αν υπάρχει διαδικασία Ito Xt που την ικανοποιεί. Αν οι b, σ είναι ανεξάρτητες του χρόνου τότε οι λύσεις των εξισώσεων αυτής της μορφής λέγονται διαδικασίες διάχυσης. Στοχαστικές διαφορικές εξισώσεις χρησιμοποιούνται για την μοντελοποίηση συστημάτων και φαινομένων που περιέχουν κάποιου είδους τυχαιότητας. Τέτοια προβλήματα προκύπτουν σε πολλά φυσικά φαινόμενα και σε θέματα οικονομικών (μοντελοποίηση μετοχών, μοντέλα επιτοκίων στα χρηματοοικονομικά). المعادلة التفاضلية التصادفية (بالإنجليزية: Stochastic differential equation)‏ (SDE) هي معادلة تفاضلية يكون فيها واحد أو أكثر من الحدود عملية تصادفية، مما يؤدي إلى حل وهو أيضًا عملية تصادفية. تُستخدم "SDEs" لنمذجة ظواهر مختلفة مثل أسعار الأسهم غير المستقرة أو الأنظمة الفيزيائية الخاضعة للتقلبات الحرارية. عادةً ما تحتوي SDEs على متغير يمثل ضجيج أبيض عشوائي محسوب كمشتق من الحركة البراونية أو عملية فينر. ومع ذلك، هناك أنواع أخرى من السلوك العشوائي ممكنة، مثل عمليات القفز. المعادلات التفاضلية العشوائية مرتبطة بالمعادلات التفاضلية التصادفية. 確率微分方程式（かくりつびぶんほうていしき、英: Stochastic differential equation）とは、1つ以上の項が確率過程である微分方程式であって、その結果、解自身も確率過程となるものである。一般的に、確率微分方程式はブラウン運動（ウィーナー過程）から派生すると考えられる白色雑音を組み込むが、不連続過程の様な他の無作為変動を用いることも可能である。
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