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Stochastic differential equation — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Stochastic_differential_equation
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T14:37:05.776Z
SHA-256 of the archived text: ffbc2a2a478c172255862bc7bcb561949d4398d534791a4972e611f8eb5574f7
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Stochastic differential equation — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Stochastic_differential_equation (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_3be5555ea3bf (Metraipolis archive dc_3be5555ea3bf, sha256 ffbc2a2a478c172255862bc7bcb561949d4398d534791a4972e611f8eb5574f7)

BibTeX

@misc{dc3be5555ea3bf,
  title = {Stochastic differential equation — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Stochastic_differential_equation},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_3be5555ea3bf; sha256 ffbc2a2a478c172255862bc7bcb561949d4398d534791a4972e611f8eb5574f7},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Stochastic_differential_equation. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as prices of listed company shares, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the distributional derivative of a Brownian motion or more generally a semimartingale. However, other types of random behaviour are possible, such as jump processes like Lévy processes or semimartingales with jumps. Stochastic differential equations are in general neither differential equations nor random differential equations. Random differential equations are conjugate to stochastic differential equations. Stochastic differential equations can also be extended to differential manifolds.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «differential equation»).
Fonte: Wikipedia in inglese, voce «Stochastic differential equation» — https://en.wikipedia.org/wiki/Stochastic_differential_equation
Wikidata Q1545585 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q1545585
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Stochastic_differential_equation?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1369949023, consultata il 2026-10-15T13:58:38.635Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 81c53745fd75e38adbaa76fa8665b0d2a9aec0219534d895022f20aa0af14cc5