We consider a new class of one-dimensional diffusion processes with self-similar random potentials. The self-similar random potential has different exponents to the left and the right hand sides of the origin. We show that, because of the difference between the two exponents, the long-time behaviors of our process on the left and the right hand sides of the origin are quite different from each other.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics