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On Global Existence of Solutions of SDE's with Singular Drift

✍ Scribed by Rainer Höhnle

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
741 KB
Volume
179
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 motion under the probability measure Q, and σ is a strictly optional time (i.e., stopping time) such that the above equation is satisfied for all t < σ. Such a local solution was constructed by the author in an earlier paper under very mild conditions on b. In this paper we give criteria for the global existence of the solution, i. e., for Q(σ = ∞) = 1.

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