January, 2009

Articles:

  1. A unification of Strassen's law and Levy's modulus of continuity, Z.Wahrsch., 56 (1981), 163-179.
  2. A characterization of BMO and BMOp, Studia. Math., 72 (1982), 47-57.
  3. Exit times of diffusions, Proceedings of the Conference on Martingale Theory, Cleveland, Springer-Verlag (1982).
  4. (with F. Weissler) Hypercontractivity for the heat semigroup for ultraspherical polynomials on the n-sphere, J. Functional Analysis, (2) 48 (1982), 262-283.
  5. (Announcement) (with S. Goldberg) Brownian motion, geometry, and generalizations of Picard's little theorem, Bull. Amer. Math. Soc., 7 (1982), 259-263.
  6. Strassen's law for local time, Z. Wahrsch, 63 (1983), 29-41.
  7. (with S. Goldberg) Brownian motion, geometry, and generalizations of Picard's little theorem, Ann. Probab., 11 (1983), 833-846.
  8. (with F. Weissler) Single point blow-up for a nonlinear heat equation. Indiana U. Math. J., 34 (1985), 881-913.
  9. (with M. Cranston) A review of recent and older results on the absolute continuity of harmonic measure. (Proceedings of a Conference on Stochastic Differential Geometry) AMS Contemporary Mathematics Series, v.73, (1988), 9-20.
  10. A counterexample concerning Brownian motion on manifolds. (Proceedings of a Conference on Stochastic Differential Geometry) AMS Contemporary Mathematics Series, v.73, (1988), 217-222.
  11. (with Li Liu) On the extinction of measure-valued critical branching Brownian motion, Ann. Probab., 17, (1989).
  12. Probability and the Equivalence of Generalized Hp Spaces, Indiana U. Math. J., 38, 4 (1989).
  13. A connection between Strassen's and Donsker-Varadhan's laws of the iterated logarithm, Probab. Th. Related Fields, 87, 365-388 (1991).
  14. Limit results for two stochastic partial differential equations, Stochastics, 37, 3, 175-199, (1991).
  15. On the support of solutions to the heat equation with noise, Stochastics, 37, 4, 225-246, (1991).
  16. Long time existence for the heat equation with a noise term, Probab. Th. and Related Fields, 90, 505-518, (1991).
  17. (with E. Perkins) The compact support property for solutions to the heat equation with noise, Probab. Th. Rel. Fields, 93, 325-358 (1992).
  18. Coupling and invariant measures for the heat equation with noise term, Ann. Probab., 21, 4, 2189-2199, (1993).
  19. A modulus for the 3-dimensional wave equation with noise: dealing with a singular kernel, Canadian J. Math., 45, 6, 1263-1275, (1993).
  20. (with R. Sowers) Blow-up for the heat equation with a noise term. Probab. Th. Rel. Fields., 97, 287-320, (1993).
  21. (with R. Tribe) (summary) A stochastic PDE arising as the limit of a long-range contact process, and its phase transition, Proceedings of a conference in probability at Montreal, CRM Proceed ings and Lecture Notes, vol. 5, 1994, 175-178.
  22. (with R. Tribe) A phase transition for a stochastic PDE related to the contact process, Probab. Th. Rel. Fields, 100, 2, 131-156, (1994).
  23. (with R. Sowers) Travelling waves for the KPP equation with noise, J. Functional Anal., 128, 439-498, (1995).
  24. (with R. Sowers) (summary) Travelling wares for the KPP equation with noise. Proceedings of Symposia in Pure Mathematics, 57, 603-609, (1995).
  25. (with D. Dawson, K. Fleischmann and Yi Li) Singularity of super-Brownian local time at a point catalyst, Ann. Probab., 23, 37-55, (1995).
  26. (with D. Dawson and Yi Li) The support of measure-valued branching processes in a random environment, Ann. Probab., 23, 4, 1692-1718, (1995).
  27. (with R. Tribe) Stochastic p.d.e.'s arising from the long range contact and long range voter models, Probab. Th. Rel. Fields, 102, 4, 519-546, (1995).
  28. Singular initial conditions for the heat equation with noise, Ann. Probab., 24, 1, 377-398, (1996).
  29. Long time existence for the wave equation with a noise term, Ann. Probab., 25, 1, 133-151 (1997).
  30. (with K. Fleischmann) A super-Brownian motion with a locally infinite catalyst, Probab. Th. Rel. Fields, 107, 3, 325-358, (1997).
  31. (with R. Tribe) Finite width for a random stationary interface, Electronic J. Probab., 2, 7, 1-27, (1997).
  32. Long-time existence for signed solutions of the heat equation with a noise term, Probab. Th. Rel. Fields, 110, 51-68, (1998).
  33. The heat equation with Levy noise, Stoch. Proc. and Appl., 74, 67-82 (1998).
  34. (with E. Pardoux) The critical exponent for a stochastic PDE to hit zero. Stochastic analysis, control, optimization and applications, 325--338, Systems Control Found. Appl., Birkhäuser Boston, Boston, MA, 1999.
  35. (with K. Fleischmann) Finite time extinction of catalytic branching processes. Stochastic Models, Proceedings of the International Conferenence on Stochastic Models, Ottawa, Canada, June 10-13, 1998, edited by L.G. Gorostiza and B.G. Ivanoff, CMS Conference Proceedings, Vol. 26, AMS and CMS, Providence RI, 125-140.
  36. (with E. Perkins) Extinction for two parabolic stochastic PDE's on the lattice, Ann. Inst. Henri Poincare, 36, 301-338, (2000).
  37. (with D. Dawson and K. Fleischmann) Finite time extinction of superprocesses with catalysts, Ann. Probab., 28, 2, 603-642, (2000).
  38. The critical parameter for the heat equation with a noise term to blow up in finite time, Ann. Probab., 28, 4, 1735-1746, (2000).
  39. A Measure-Valued Process Related to the Parabolic Anderson Model, Proceedings of a Conference at Ascona, (2001).
  40. (with R. Tribe) Hitting properties of a random string, Electronic J. Probab., 7, paper 10, 1-29, (2002)
  41. (with R. Dalang) Some non-linear s.p.d.e.'s that are second order in time, Electronic J. Probab., 8, paper 1, 1-21, (2003)
  42. (with C. Doering and P. Smereka) Noisy wavefront propagation in the Fisher-Kolmogorov-Petrovsky-Piscounov equation, in UpoN 2002: Proceedings of the 3rd International Conference on Unsolved Problems of Noise, NIH, Bethesda, ed. S. Bezrukov (American Institute of Physics, 2003). (pp 523-530)
  43. (with C. Doering and P. Smereka) Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality, Phys. A 325, 243-259 (2003).
  44. (with R. Tribe) A singular parabolic Anderson model, Electronic J. Prob., 9, paper 5, 98-144, (2004).
  45. (with K. Fleischmann) Super-Brownian motion with extra birth at one point, SIAM J. Math. Anal., 36, 3, 740-772, (2004).
  46. (with A. Stan) A stochastic Heisenberg inequality, in Quantum Information and Complexity, Proceedings of the Meijo Winter School 2003, edited by T. Hida, K. Saito, and Si Si, World Scientific, Singapore, 362-375, (2004).

  47. (with A. Stan) A Heisenberg inequality for stochastic integrals, J. of Theoretical Probability, 18, 2, 291-315, (2005).
  48. (with L. Mytnik and A. Stan) The heat equation with time-independent multiplicative stable L\'evy noise, Stoch. Proc. Appl., 116, 1, 70-100, (2006).

  49. (with R. Dalang and L. Zambotti) Hitting properties of s.p.d.e.'s with reflection, Ann. Probab., 34, 4, 1423-1450, (2006).

  50. (with K. Fleischmann and P. Vogt) On the large scale behavior of superbrownian motion with a single point source, Comm. Stoch. Anal., 1, 1, 19-28, (2007).
  51. (with R. Dalang and R. Tribe) A Feynman-Kac formula for the deterministic and stochastic wave equations and other p.d.e.'s, Trans. Amer. Math. Soc. 360, 4681-4703, (2008).
  52. (with D. Nualart) Regularity of the density for the stochastic heat equation, Electronic J. Prob., 13, paper 74, 2248-2258, (2008).
  53. (with L. Mytnik and J. Quastel) Small noise asymptotics of traveling waves, Markov Proc. Rel. Fields, 14, 3, 333-342, (2008).
  54. (with Z. Wu) A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand, Electronic Comm. Prob., 14, 55-65, (2009).
  55. Some tools and results for parabolic stochastic partial differential equations, in Proceedings of a summer school in probability, University of Utah, Editors Davar Khoshnevisan and Firas Rassoul-Agha, Lecture Notes in Mathematics number 1962, Springer, p. 111-144 (2009).
  56. (with K. Lee) On the discrete heat equation taking values on a tree, Proc. Amer. Math. Soc., 137, 1467-1478, (2009).

To Appear:

  1. (with K. Lee and J. Xiong) Some properties for superprocess under a stochastic flow, Ann. Poincare.
  2. (with R. Dalang) Intermittency properties in a hyperbolic Anderson model, Ann. Poincare.

Submitted:

  1. (with R. Tribe) A phase diagram for a stochastic reaction diffusion system, Prob. Th. Rel. Fields.

In Preparation: