In our talk we will discuss two-dimensional Lévy processes with reflection at the boundaries of the positive quadrant in the non-standard regime when the mean of the original process is negative but the reflection vectors point away from the origin so that the reflected process escapes to infinity along one of the axes.

First, it will be shown that, under rather general conditions, such behaviour is certain and each component can dominate the other with positive probability for any given starting position, and also the invariance principle will be established, providing justification for the use of reflected Brownian motion as an approximate model.

Next, for both the compound Poisson and the Brownian models, we will derive the corresponding kernel equation for the Laplace transform of the probability that the reflected stochastic process escapes to infinity along the first axis as a function of the starting position.

Finally, the solution of both equations will be obtained by means of the boundary value problem analysis, which also yields the domination probability when the process starts at the origin.

The talk is based on joint work with S. Franceschi and J. Ivanovs.

The talk will be given on Zoom. Please, contact the organizers for more information.