# Publications

## Submitted

- (with L. Mytnik and E. Perkins) On the Boundary of the Support of Super-Brownian Motion, Ann. Prob.
- (with R. Dalang and Y. Xiao) Polarity of points for Gaussian random fields, Ann. Prob.

## To Appear

- (with D. Khoshnevisan and M. Joseph) Strong invariance and noise comparison principles for some parabolic SPDEs, Ann. Prob.

## Published

- (with R. Dalang) Multiple points of the Brownian sheet in critical dimensions, Ann. Prob. 43, 4, 1577-1593 (2015).
- Lecture notes on SPDE from the point of view of particle systems and duality, in Stochastic Analysis: A Series of Lectures, Birkhauser, Progress in Probability, 68, 271-295 (2015)
- (with L. Mytnik and E. Perkins) Nonuniqueness for a parabolic SPDE
with
\frac{3}{4}-\varepsilon -H"older diffusion coefficients, Ann. Prob. 42, 5, 2032-2112 (2014). - (with G. Richards) Can solutions of the one-dimensional wave equation with nonlinear multiplicative noise blow up?, Open Prob. Math 2, 1-4 (2014).
- (with S. Starr) The length of the longest increasing subsequence of a random Mallows permutation, J of Th. Prob. 26, 2, 514-540 (2013).
- (with A. Wei, A. Gomez, K. Lee, and J. Xiong) Strong uniqueness for an SPDE via backward doubly stochastic differential equations, Stat. and Prob. Letters 83, 2186-2190 (2013).
- (with L. Mytnik and J. Quastel) Effect of noise on front propagation in reaction-diffusion equations of KPP type, Invent. Math. 184, 2, 405-453 (2011).
- (With R. Tribe) A phase diagram for a stochastic reaction diffusion system, Prob. Th. Rel. Fields, 149, 3-4, 561-637 (2011).
- (with Y. Bakhtin) Solutions of Semilinear Wave Equation via Stochastic Cascades, Comm. Stoch. Anal., 4, 3, 425-431, (2010).
- (with K. Burdzy and E. Perkins) Non-uniqueness for non-negative solutions of parabolic stochastic partial differential equations, Ill. J. Math., 54, 4, 1481-1507 (2010).
- (with K. Kim and R. Sowers) A stochastic moving boundary value problem, Ill. J. Math., 54, 3, 927-962 (2010).
- (with K. Lee and J. Xiong) Some properties for superprocess under a stochastic flow, Ann. Poincare, 45, 2, 477-490 (2009).
- (with R. Dalang) Intermittency properties in a hyperbolic Anderson model, Ann. Poincare, 45, 4, 1150-1164 (2009).
- (with K. Lee) On the discrete heat equation taking values on a tree, Proc. Amer. Math. Soc., 137, 1467-1478, (2009).
- 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).
- (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).
- (with D. Nualart) Regularity of the density for the stochastic heat equation, Electronic J. Prob., 13, paper 74, 2248-2258, (2008).
- (with L. Mytnik and J. Quastel) Small noise asymptotics of traveling waves, Markov Proc. Rel. Fields, 14, 3, 333-342, (2008).
- (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).
- (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).
- (with R. Dalang and L. Zambotti) Hitting properties of s.p.d.e.’s with reflection, Ann. Probab., 34, 4, 1423-1450, (2006).
- (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).
- (with A. Stan) A Heisenberg inequality for stochastic integrals, J. of Theoretical Probability, 18, 2, 291-315, (2005).
- (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).
- (with K. Fleischmann) Super-Brownian motion with extra birth at one point, SIAM J. Math. Anal., 36, 3, 740-772, (2004).
- (with R. Tribe) A singular parabolic Anderson model, Electronic J. Prob., 9, paper 5, 98-144, (2004).
- (with C. Doering and P. Smereka) Interacting particles, the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation, and duality, Phys. A 325, 243-259 (2003).
- (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)
- (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)
- (with R. Tribe) Hitting properties of a random string, Electronic J. Probab., 7, paper 10, 1-29, (2002)
- (with R. Tribe) A Measure-Valued Process Related to the Parabolic Anderson Model, Proceedings of a Conference at Ascona, (2001).
- The critical parameter for the heat equation with a noise term to blow up in finite time, Ann. Probab., 28, 4, 1735-1746, (2000).
- (with D. Dawson and K. Fleischmann) Finite time extinction of superprocesses with catalysts, Ann. Probab., 28, 2, 603-642, (2000).
- (with E. Perkins) Extinction for two parabolic stochastic PDE’s on the lattice, Ann. Inst. Henri Poincare, 36, 301-338, (2000).
- (with K. Fleischmann) Finite time extinction of catalytic branching processes. Stochastic Models, Proceedings of the International Conference 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.
- (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., Birkhauser Boston, Boston, MA, 1999.
- The heat equation with Levy noise, Stoch. Proc. and Appl., 74, 67-82 (1998).
- Long-time existence for signed solutions of the heat equation with a noise term, Probab. Th. Rel. Fields, 110, 51-68, (1998).
- (with R. Tribe) Finite width for a random stationary interface, Electronic J. Probab., 2, 7, 1-27, (1997).
- (with K. Fleischmann) A super-Brownian motion with a locally infinite catalyst, Probab. Th. Rel. Fields, 107, 3, 325-358, (1997).
- Long time existence for the wave equation with a noise term, Ann. Probab., 25, 1, 133-151 (1997).
- Singular initial conditions for the heat equation with noise, Ann. Probab., 24, 1, 377-398, (1996).
- (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).
- (with D. Dawson and Yi Li) The support of measure-valued branching processes in a random environment, Ann. Probab., 23, 4, 1692-1718, (1995).
- (with D. Dawson, K. Fleischmann and Yi Li) Singularity of super-Brownian local time at a point catalyst, Ann. Probab., 23, 37-55, (1995).
- (with R. Sowers) (summary) Travelling wares for the KPP equation with noise. Proceedings of Symposia in Pure Mathematics, 57, 603-609, (1995).
- (with R. Sowers) Travelling waves for the KPP equation with noise, J. Functional Anal., 128, 439-498, (1995).
- (with R. Tribe) A phase transition for a stochastic PDE related to the contact process, Probab. Th. Rel. Fields, 100, 2, 131-156, (1994).
- (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.
- (with R. Sowers) Blow-up for the heat equation with a noise term. Probab. Th. Rel. Fields., 97, 287-320, (1993).
- A modulus for the 3-dimensional wave equation with noise: dealing with a singular kernel, Canadian J. Math., 45, 6, 1263-1275, (1993).
- Coupling and invariant measures for the heat equation with noise term, Ann. Probab., 21, 4, 2189-2199, (1993).
- (with E. Perkins) The compact support property for solutions to the heat equation with noise, Probab. Th. Rel. Fields, 93, 325-358 (1992).
- Long time existence for the heat equation with a noise term, Probab. Th. and Related Fields, 90, 505-518, (1991).
- On the support of solutions to the heat equation with noise, Stochastics, 37, 4, 225-246, (1991).
- Limit results for two stochastic partial differential equations, Stochastics, 37, 3, 175-199, (1991).
- A connection between Strassen’s and Donsker-Varadhan’s laws of the iterated logarithm, Probab. Th. Related Fields, 87, 365-388 (1991).
- Probability and the Equivalence of Generalized Hp Spaces, Indiana U. Math. J., 38, 4 (1989).
- (with Li Liu) On the extinction of measure-valued critical branching Brownian motion, Ann. Probab., 17, (1989).
- A counterexample concerning Brownian motion on manifolds. (Proceedings of a Conference on Stochastic Differential Geometry) AMS Contemporary Mathematics Series, v.73, (1988), 217-222. Stochastic Differential Geometry) AMS Contemporary Mathematics Series, v.73, (1988), 9-20.
- (with M. Cranston) A review of recent and older results on the absolute continuity of harmonic measure. (Proceedings of a Conference on
- (with F. Weissler) Single point blow-up for a nonlinear heat equation. Indiana U. Math. J., 34 (1985), 881-913.
- (with S. Goldberg) Brownian motion, geometry, and generalizations of Picard’s little theorem, Ann. Probab., 11 (1983), 833-846.
- Strassen’s law for local time, Z. Wahrsch, 63 (1983), 29-41.
- (Announcement) (with S. Goldberg) Brownian motion, geometry, and generalizations of Picard’s little theorem, Bull. Amer. Math. Soc., 7 (1982), 259-263.
- (with F. Weissler) Hypercontractivity for the heat semigroup for ultraspherical polynomials on the n-sphere, J. Functional Analysis, (2) 48 (1982), 262-283.
- Exit times of diffusions, Proceedings of the Conference on Martingale Theory, Cleveland, Springer-Verlag (1982).
- A characterization of BMO and BMOp, Studia. Math., 72 (1982), 47-57.
- A unification of Strassen’s law and Levy’s modulus of continuity, Z.Wahrsch., 56 (1981), 163-179.

Page owner: Carl Mueller

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