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Vol.44.No.1(67) >

 
Title :確率微分方程式の逐次近似解の収束条件に関する考察
Authors :川畑 茂徳
Issue Date :Sep-2011
Abstract :We consider the problem of successive approximation for solutions of stochastic differential equations. It is well known that in Ito’s classical theory of stochastic differential equations with Lipschitz continuous coefficients, the successive approximation method plays an essential role in the construction of solutions as well as in the uniqueness problem. We show that conditions which guarantee pathwise uniqueness of solutions also imply the convergence of successive approximations to the solutions in quadratic mean. The proof is due to a result from the theory of ordinary differential equations. To ensure the pathwise uniquness of the solutions we need to impose the conditions on the variation of the function σ(t,x)relative to (t,x)
Type Local :紀要論文
ISSN :02876620
Publisher :福岡工業大学
URI :http://hdl.handle.net/11478/1287
citation :福岡工業大学研究論集
44
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Citation :福岡工業大学研究論集 Vol.44 no.1 p.13 -16
Appears in Collections:Vol.44.No.1(67)

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