48 citations · 117 across the 21 of their papers we have counts for
5 papers · 2 filters
Non-local Dirichlet Forms and Symmetric Jump Processes
M. T. Barlow, R. F. Bass, Z. -Q. Chen. +1
We consider the symmetric non-local Dirichlet form given by \[ E (f,f)=\int_{R^d} \int_{R^d} (f(y)-f(x))^2 J(x,y) dx dy \] with the closure of the set of functio…
Frequent points for random walks in two dimensions
Richard F. Bass, Jay Rosen
For a symmetric random walk in which does not necessarily have bounded jumps we study those points which are visited an unusually large number of times. We prove the analogue…
Moderate deviations for the range of planar random walks
Richard F. Bass, Xia Chen, Jay Rosen
Given a symmetric random walk in with finite second moments, let be the range of the random walk up to time . We study moderate deviations for and $E R_…
The submartingale problem for a class of degenerate elliptic operators
Richard F. Bass, Alexander Lavrentiev
We consider the degenerate elliptic operator acting on functions on : \[ L f(x)=\sum_{i=1}^d a_i(x) x_i^{α_i} \frac{\partial^2 f}{\partial x_i^2} (x) +\sum_{i=1…
Pathwise uniqueness for a degenerate stochastic differential equation
Richard F. Bass, Krzysztof Burdzy, Zhen-Qing Chen
We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation \[dX_t=|X_t|^α dW_t,\] where is a one-dimensional…