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Stochastic differential equations with fractal noise

✍ Scribed by M. Zähle

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
162 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Stochastic differential equations in ℝ^n^ with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W^β^~2~ for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution procedure is developed which combines the stochastic Itô calculus with fractional calculus via norm estimates of associated integral operators in W^α^ ~2~ for 0 < α < 1. Linear equations are considered as a special case. This approach leads to fast computer algorithms basing on Picard's iteration method. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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