Abstract. We give a simple method to approximate multidimensional exponentially tempered stable processes and show that the approximating process converges in the Skorokhod topology to the tempered process. The approximation is based on the generation of a random angle and a random variable with a lower dimensional Lévy measure. We then show that if an arbitrarily small normal random variable i...

We prove a quenched functional central limit theorem for one-dimensional random walk driven by simple symmetric exclusion process. This model can be viewed as special case of the in balanced environment, which weak is constructed function invariant measure environment from walk. bypass need to show existence this measure. Instead, we find quadratic variation and give an explicit formula it.