Stochastic calculus for tempered fractional Brownian motion and stability for SDEs driven by TFBM

The objective of this article is to introduce and study Itô type stochastic integrals with respect to tempered fractional Brownian motion (TFBM) of Hurst index H∈(12,1) and tempering parameter λ>0, by using the Wick product. The main tools are fractional calculus and Malliavin calculus. The Itô formula for this stochastic integral is established for the Itô type processes driven by TFBM. Based on this new Itô formula, we analyze the stability of stochastic differential equations driven by TFBM in the sense of p-th moment. A numerical example is given to illustrate our stability results.