Resolution trajectorielle et analyse numerique des equations differentielles stochastiques

Abstract

Let (ξt) be the solution of the S.D.E. (E) of Section 1. Doss [3] has shown the existence of a difFerentiable function h and of a differentiate process parametrized by the process W,γ(W,t), such that: ξt = h(γ(W, t), Wt). For all continuous functions u, Xt is defined by: Xt = h(γ(u, t) ut). We develop a scheme of approximation of Xt (Theorems 2-6 and 3-4). This scheme has th following properties:? 1)it does not explicitly involve γ or h; this property is crucial, because,generally, h is not explicitly known, and its numerical approximation would be costly. 2)it converges to Xt, provided that u has bounded quadratic variation. 3)for u = W, it coincides with a scheme proposed by Milshtein [6] for quadratic-mean approximation. Further, we give an estimate of the error due to this scheme.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 42 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.