I am interested in spatial stochastic models, in particular in diffusions, branching diffusions, superprocesses, and processes in random media. Certain linear and nonlinear partial differential equations are closely connected to these research areas. My broader interest lies in probability theory in general.
- Local extinction versus local exponential growth for spatial branching processes. (with Kyprianou, A. E.) Ann. Probab. 32 (2004), no. 1A, 78--99.
- Uniqueness/nonuniqueness for nonnegative solutions of second-order parabolic equations of the form u_ t=Lu+Vu-\gamma u^p in R^n. (with Pinsky, R. G.) J. Differential Equations 192 (2003), no. 2, 396--428.
- A scaling limit theorem for a class of superdiffusions. (with Turaev, D.) Ann. Probab. 30 (2002), no. 2, 683--722.
- On the construction and support properties of measure-valued diffusions on D\subseteqR^d with spatially dependent branching. (with Pinsky, R. G.) Ann. Probab. 27 (1999), no. 2, 684--730.
- The asymptotic behavior of the principal eigenvalue for small perturbations of critical one-dimensional Schrodinger operators with V(x)=l±/x^2 for ±x>>1. (with Pinsky, R. G.) J. Funct. Anal. 133 (1995), no. 2, 501--515.