Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type
The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutral stochastic differential equations, we impose a w...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/10/1613 |
| Summary: | The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutral stochastic differential equations, we impose a weakened H<inline-formula><math display="inline"><semantics><mover accent="true"><mi mathvariant="normal">o</mi><mo>¨</mo></mover></semantics></math></inline-formula>lder condition and a weakened linear growth condition. Stochastic results are obtained for the theory of the existence and uniqueness of the solution. We first show that the conditions guarantee the existence and uniqueness; then, we show some exponential estimates for the solutions. |
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| ISSN: | 2073-8994 |