48 citations · 71 across the 7 of their papers we have counts for
8 papers · 1 filter
Symmetric Markov chains on with unbounded range
Richard F. Bass, Takashi Kumagai
We consider symmetric Markov chains on where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform sec…
Large deviations for renormalized self-intersection local times of stable processes
Richard Bass, Xia Chen, Jay Rosen
We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index β\in (2d/3,d]. We find a difference between the upper and low…
Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks
Richard F. Bass, Xia Chen, Jay Rosen
Let B_n be the number of self-intersections of a symmetric random walk with finite second moments in the integer planar lattice. We obtain moderate deviation estimates for B_n - E…
Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm
Richard F. Bass, Xia Chen
If β_t is renormalized self-intersection local time for planar Brownian motion, we characterize when Ee^{γβ_1} is finite or infinite in terms of the best constant of a Gagliardo-Ni…
Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type
Siva R. Athreya, Richard F. Bass, Maria Gordina +1
We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i x_i b_i(x) \frac{\del f}{\del x_i}(x).$$ We…
An almost sure invariance principle for renormalized intersection local times
Richard F. Bass, Jay Rosen
Let β_k(n) be the number of self-intersections of order k, appropriately renormalized, for a mean zero random walk X_n in Z^2 with 2+δmoments. On a suitable probability space we ca…