The Harnack inequality for stochastic differential equation driven by G-Brownian motion with multiplicative noise is derived by means of the coupling by change of measure,which extends the corresponding results derive...The Harnack inequality for stochastic differential equation driven by G-Brownian motion with multiplicative noise is derived by means of the coupling by change of measure,which extends the corresponding results derived in Wang(Probab.Theory Related Fields 109:417–424)under the linear expectation.Moreover,we generalize the gradient estimate under nonlinear expectation appeared in Song(Sci.China Math.64:1093–1108).展开更多
The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes ...The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes the existing ones for SDEs driven by the standard Brownian motion.展开更多
In this paper,the Harnack inequality for G-SDEs with degenerate noise is derived by the method of coupling by change of the measure.Moreover,for any bounded and continuous function f,the gradient estimate∣∇P_(t)f∣≤...In this paper,the Harnack inequality for G-SDEs with degenerate noise is derived by the method of coupling by change of the measure.Moreover,for any bounded and continuous function f,the gradient estimate∣∇P_(t)f∣≤c(p,t)(Pt|f|p)^(1/p),p>1,t>0 is obtained for the associated nonlinear semigroup P¯t.As an application of the Harnack inequality,we prove the existence of the weak solution to degenerate G-SDEs under some integrable condition.Finally,an example is presented.All of the above results extend the existing ones in the linear expectation setting.展开更多
In this paper,Wang's Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are established.The results generalize the ones in the linear expectation sett...In this paper,Wang's Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are established.The results generalize the ones in the linear expectation setting.Moreover,some applications are also given.展开更多
In this paper,the Harnack and shift Harnack inequalities for functional G-SDEs with degenerate noise are derived by the method of coupling by change of measure.Moreover,the gradient estimate for the associated nonline...In this paper,the Harnack and shift Harnack inequalities for functional G-SDEs with degenerate noise are derived by the method of coupling by change of measure.Moreover,the gradient estimate for the associated nonlinear semigroup P_(t) is obtained.All of the above results extend the existed results in linear expectation setting.展开更多
文摘The Harnack inequality for stochastic differential equation driven by G-Brownian motion with multiplicative noise is derived by means of the coupling by change of measure,which extends the corresponding results derived in Wang(Probab.Theory Related Fields 109:417–424)under the linear expectation.Moreover,we generalize the gradient estimate under nonlinear expectation appeared in Song(Sci.China Math.64:1093–1108).
文摘The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes the existing ones for SDEs driven by the standard Brownian motion.
基金supported by National Natural Science Foundation of China(Grant No.11801406).
文摘In this paper,the Harnack inequality for G-SDEs with degenerate noise is derived by the method of coupling by change of the measure.Moreover,for any bounded and continuous function f,the gradient estimate∣∇P_(t)f∣≤c(p,t)(Pt|f|p)^(1/p),p>1,t>0 is obtained for the associated nonlinear semigroup P¯t.As an application of the Harnack inequality,we prove the existence of the weak solution to degenerate G-SDEs under some integrable condition.Finally,an example is presented.All of the above results extend the existing ones in the linear expectation setting.
基金supported by the National Natural Science Foundation of China (Nos. 11801406)
文摘In this paper,Wang's Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are established.The results generalize the ones in the linear expectation setting.Moreover,some applications are also given.
文摘In this paper,the Harnack and shift Harnack inequalities for functional G-SDEs with degenerate noise are derived by the method of coupling by change of measure.Moreover,the gradient estimate for the associated nonlinear semigroup P_(t) is obtained.All of the above results extend the existed results in linear expectation setting.
