Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations.
Appleby, John A.D., Kelly, Cónall (2004)
Electronic Communications in Probability [electronic only]
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Appleby, John A.D., Kelly, Cónall (2004)
Electronic Communications in Probability [electronic only]
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Liu, Yue, Meng, Xuejing, Wu, Fuke (2010)
International Journal of Stochastic Analysis
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Tudor, Ciprian A. (2004)
Journal of Applied Mathematics and Stochastic Analysis
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Ji, Chunyan, Jiang, Daqing, Liu, Hong, Yang, Qingshan (2010)
Mathematical Problems in Engineering
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Swishchuk, Anatoliy, Xu, Li (2011)
International Journal of Stochastic Analysis
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Appleby, John A.D. (2002)
Electronic Communications in Probability [electronic only]
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Fu, Xianlong (2009)
Journal of Inequalities and Applications [electronic only]
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Appleby, John A.D., Flynn, Aoife (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Sonoc, C. (1998)
Portugaliae Mathematica
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Krystyna Twardowska, Tomasz Marnik, Monika Pasławska-Południak (2003)
International Journal of Applied Mathematics and Computer Science
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A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.
Balachandran, K., Kim, J.-H. (2006)
Journal of Applied Mathematics and Stochastic Analysis
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Stoyanov, Jordan, Botev, Dobrin (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Svetlana Janković, Miljana Jovanović (2000)
Publications de l'Institut Mathématique
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