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On approximation of solutions of multidimensional SDE's with reflecting boundary conditions

✍ Scribed by Leszek Słomiński


Book ID
107950461
Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
978 KB
Volume
50
Category
Article
ISSN
0304-4149

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📜 SIMILAR VOLUMES


Some remarks on approximation of solutio
✍ Leszek Słomiński 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 372 KB

Let D be either a convex domain in ~a or a domain satisfying the conditions (A) and (B) considered by and . We estimate the rate of convergence for Euler scheme for stochastic differential e~luations in D with normal reflection at the boundary of the form where W is a d-dimensional Wiener process.

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## Abstract Let __b__ be a Borel measurable IR^d^ ‐ valued function, defined on some Borel subset of IR^d^. Consider the __d‐__ dimensional SDEmagnified imagewith singular drift __b__. A local solution (up to σ) is a tuple (__X, W__, Q,σ) where __X__ is a stochastic process, __W__ is a Brownian mot

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✍ T. Jankowski 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 386 KB

The quasilinearization method is used for nonlinear ordinary differential equations with nonlinear boundary conditions. Given are sufficient conditions when corresponding monotone sequences converge to the unique solution and this convergence is quadratic. (~ 2004 Elsevier Ltd. All rights reserved.