Kloeden, Peter E.; Lorenz, Thomas Stochastic differential equations with nonlocal sample dependence. (English) Zbl 1205.60131 Stochastic Anal. Appl. 28, No. 6, 937-945 (2010). Summary: Stochastic ordinary differential equations are investigated for which the coefficients depend on nonlocal properties of the current random variable in the sample space such as the expected value or the second moment. The approach here covers a broad class of functional dependence of the right-hand side on the current random state and is not restricted to pathwise relations. Existence and uniqueness of solutions is obtained as a limiting process by freezing the coefficients over short time intervals and applying existence and uniqueness results and appropriate estimates for stochastic ordinary differential equations. Cited in 23 Documents MSC: 60H35 Computational methods for stochastic equations (aspects of stochastic analysis) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H25 Random operators and equations (aspects of stochastic analysis) Keywords:existence and uniqueness theorems; Itô stochastic differential equations; nonlocal dependence; strong solutions PDFBibTeX XMLCite \textit{P. E. Kloeden} and \textit{T. Lorenz}, Stochastic Anal. Appl. 28, No. 6, 937--945 (2010; Zbl 1205.60131) Full Text: DOI References: [1] DOI: 10.1023/A:1016673307045 · Zbl 1004.37034 · doi:10.1023/A:1016673307045 [2] DOI: 10.1098/rspa.2007.0055 · Zbl 1140.65015 · doi:10.1098/rspa.2007.0055 [3] Lorenz Th., Mutational Analysis: A Joint Framework for Dynamical Systems In and Beyond Vector Spaces (2009) [4] Lorenz Th., Bol. Soc. Esp. Mat. Apl. 51 pp 99– (2009) [5] Xuerong M., Stochastic Differential Equations and Applications (2008) · Zbl 1157.60061 [6] Hernandez E., J. Appl. Math. Stoch. Anal (2007) [7] Friedman A., Stochastic Differential Equations and Applications (1975) · Zbl 0323.60056 [8] Øksendal B., Stochastic Differential Equations. An Introduction with Applications (2003) [9] DOI: 10.1007/978-1-4612-0949-2 · doi:10.1007/978-1-4612-0949-2 [10] Kloeden P.E., Numerical Solution of Stochastic Differential Equations (1992) · Zbl 0752.60043 · doi:10.1007/978-3-662-12616-5 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.