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The Harnack and log Harnack inequalities for stochastic differential equation driven by $G$-Brownian motion with multiplicative noise are derived by means of coupling by change of mesure. All of the above results extend the existing ones in the linear expectation setting. Moreover, the gradient estimate generalize the nonlinear results appeared in [11].
We establish Harnack inequality and shift Harnack inequality for stochastic differential equation driven by $G$-Brownian motion. As applications, the uniqueness of invariant linear expectations and estimates on the $sup$-kernel are investigated, wher
This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated operators for
We give some a priori estimates of type sup*inf for Yamabe and prescribed scalar curvature type equations on Riemannian manifolds of dimension >2. The product sup*inf is caracteristic of those equations, like the usual Harnack inequalities for non ne
We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure exis
Following the recent work of Jiang and Lin (Linear Algebra Appl. 585 (2020) 45--49), we present more results (bounds) on Harnack type inequalities for matrices in terms of majorization (i.e., in partial products) of eigenvalues and singular values. W