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Erschienen in:
2019 | OriginalPaper | Buchkapitel
On Time-Global Solutions of SDE Having Nowhere Vanishing Initial Densities
verfasst von : Yuri E. Gliklikh
Erschienen in: Modern Methods in Operator Theory and Harmonic Analysis
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Abstract
We deal with stochastic differential equations (SDE) on the non-compact finite-dimensional manifolds and consider their solutions such that the initial values have densities nowhere equal to zero. First, we obtain a sufficient condition under which all such solutions exist on the entire half-axis \([0,\infty )\). Further, we introduce the notion of the system, generated by the above equation, continuous at infinity. A sufficient condition the latter property to be satisfied is found. Then we find the necessary and sufficient condition for existence of the above solutions on \([0,\infty )\) for the case where the corresponding system is continuous at infinity.