Harnack Inequality Of Stochastic Differential Equations Driven By Mixed Noise Of Brownian Motion And Fractional Brownian Motion

The dimension independent Harnack inequality has many applications in stochastic analysis,It is often used in various inequalities to characterize some properties of solutions of stochastic differential equations?This paper focuses on the Harnack inequality of stochastic differential equations driven by mixed Brownian noise,The main research results are as follows:(1)Based on the results of [1] and [4],this paper first discusses some similar methods used in the establishment of Harnack inequality in these two documents,then obtains the Harnack inequality of stochastic differential equations driven by mixed Brownian noise by using the variable measure coupling method and Girsanov transformation?(2)This paper gives some applications of power Harnack inequality and logarithmic Harnack inequality,such as strong Feller property and entropy cost inequality?...