By using the coupling method and the localization technique, we establish non-uniform gradient estimates for Markov semigroups of diffusions or stochastic differential equations driven by pure jump Le′vy noises, wher...By using the coupling method and the localization technique, we establish non-uniform gradient estimates for Markov semigroups of diffusions or stochastic differential equations driven by pure jump Le′vy noises, where the coefficients only satisfy local monotonicity conditions.展开更多
We establish sharp functional inequalities for time-changed symmetric α-stable processes on Rd with d≥1 and α∈(0,2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, whe...We establish sharp functional inequalities for time-changed symmetric α-stable processes on Rd with d≥1 and α∈(0,2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x)=(1+|x|)β with β>α we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11831014)the Program for Probability and Statistics:Theory and Application(Grant No.IRTL1704)the Program for Innovative Research Team in Science and Technology in Fujian Province University(IRTSTFJ)。
文摘By using the coupling method and the localization technique, we establish non-uniform gradient estimates for Markov semigroups of diffusions or stochastic differential equations driven by pure jump Le′vy noises, where the coefficients only satisfy local monotonicity conditions.
文摘We establish sharp functional inequalities for time-changed symmetric α-stable processes on Rd with d≥1 and α∈(0,2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x)=(1+|x|)β with β>α we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.
