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...

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Main Authors:	Mun-Jin Bae, Chan-Ho Park, Young-Ho Kim
Format:	Article
Language:	English
Published:	MDPI AG 2020-09-01
Series:	Symmetry
Subjects:	existence and uniqueness exponential estimates neutral type weakened Hölder’s condition weakened linear growth condition
Online Access:	https://www.mdpi.com/2073-8994/12/10/1613

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spelling	doaj-8819fc650ec64715942a902220eab1872020-11-25T02:23:33ZengMDPI AGSymmetry2073-89942020-09-01121613161310.3390/sym12101613Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral TypeMun-Jin Bae0Chan-Ho Park1Young-Ho Kim2Department of mathematics, Changwon National University, Changwon 641-773, KoreaDepartment of mathematics, Changwon National University, Changwon 641-773, KoreaDepartment of mathematics, Changwon National University, Changwon 641-773, KoreaThe 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.https://www.mdpi.com/2073-8994/12/10/1613existence and uniquenessexponential estimatesneutral typeweakened Hölder’s conditionweakened linear growth condition
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Mun-Jin Bae Chan-Ho Park Young-Ho Kim
spellingShingle	Mun-Jin Bae Chan-Ho Park Young-Ho Kim Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type Symmetry existence and uniqueness exponential estimates neutral type weakened Hölder’s condition weakened linear growth condition
author_facet	Mun-Jin Bae Chan-Ho Park Young-Ho Kim
author_sort	Mun-Jin Bae
title	Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type
title_short	Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type
title_full	Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type
title_fullStr	Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type
title_full_unstemmed	Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type
title_sort	conditions to guarantee the existence of the solution to stochastic differential equations of neutral type
publisher	MDPI AG
series	Symmetry
issn	2073-8994
publishDate	2020-09-01
description	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.
topic	existence and uniqueness exponential estimates neutral type weakened Hölder’s condition weakened linear growth condition
url	https://www.mdpi.com/2073-8994/12/10/1613
work_keys_str_mv	AT munjinbae conditionstoguaranteetheexistenceofthesolutiontostochasticdifferentialequationsofneutraltype AT chanhopark conditionstoguaranteetheexistenceofthesolutiontostochasticdifferentialequationsofneutraltype AT younghokim conditionstoguaranteetheexistenceofthesolutiontostochasticdifferentialequationsofneutraltype
_version_	1724858864539533312

Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type

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