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Walk-on-spheres method — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Walk-on-spheres_method
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-07T18:21:40.185Z
SHA-256 of the archived text: 4ae26125b57e4b43a5743ec3942d786b7b2b4cc8783e4de4eb0b91933287d099
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Walk-on-spheres method — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Walk-on-spheres_method (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_76ec22bc4c8f (Metraipolis archive dc_76ec22bc4c8f, sha256 4ae26125b57e4b43a5743ec3942d786b7b2b4cc8783e4de4eb0b91933287d099)

BibTeX

@misc{dc76ec22bc4c8f,
  title = {Walk-on-spheres method — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Walk-on-spheres_method},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_76ec22bc4c8f; sha256 4ae26125b57e4b43a5743ec3942d786b7b2b4cc8783e4de4eb0b91933287d099},
  year = {2026}
}

Archived text

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

In mathematics, the walk-on-spheres method (WoS) is a numerical probabilistic algorithm, or Monte-Carlo method, used mainly in order to approximate the solutions of some specific boundary value problem for partial differential equations (PDEs). The WoS method was first introduced by Mervin E. Muller in 1956 to solve Laplace's equation, and was since then generalized to other problems. It relies on probabilistic interpretations of PDEs, and simulates paths of Brownian motion (or for some more general variants, diffusion processes), by sampling only the exit-points out of successive spheres, rather than simulating in detail the path of the process. This often makes it less costly than "grid-based" algorithms, and it is today one of the most widely used "grid-free" algorithms for generating Brownian paths.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «differential equation»).
Fonte: Wikipedia in inglese, voce «Walk-on-spheres method» — https://en.wikipedia.org/wiki/Walk-on-spheres_method
Wikidata Q25303850: «Mathematical algorithm» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q25303850
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Walk-on-spheres_method?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 1368623327, consultata il 2026-11-07T18:16:27.658Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: fd831789505b3a263410d04d2f414c04e24e92164e2c283fab87416447f7c482