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A new technique for proving uniqueness of martingale problems is introduced. The method is illustrated in the context of elliptic diffusions in Rd.

- Leonid Mytnik, Edwin C. Perkins
- 2008

We prove pathwise uniqueness for solutions of parabolic stochastic pdeâ€™s with multiplicative white noise if the coefficient is HÃ¶lder continuous of index Î³ > 3/4. The method of proof is anâ€¦ (More)

- BY MARK HOLMES, Edwin C. Perkins, Edward J. Perkins
- 2006

We prove a sufficient set of conditions for a sequence of finite measures on the space of cadlag measure-valued paths to converge to the canonical measure of super-Brownian motion in the sense ofâ€¦ (More)

- Theodore Cox, Mathieu Merle, Edwin C. Perkins
- 2009

We study the stochastic spatial model for competing species introduced by Neuhauser and Pacala in two spatial dimensions. In particular we confirm a conjecture of theirs by showing that there isâ€¦ (More)

- Luke A. Roy, Jeffrey L Armstrong, +5 authors Daniel Schlenk
- Environmental toxicology and chemistry
- 2003

In July 2000, 330 individuals of three flatfish species were collected from reference locations and nine sites surrounding the outfall of the Orange County (CA, USA) Sanitation District (OCSD)â€¦ (More)

- Richard Durrett, Leonid Mytnik, Edwin C. Perkins
- 2008

We study two-type branching random walks in which the the birth or death rate of each type can depend on the number of neighbors of the opposite type. This competing species model contains variantsâ€¦ (More)

- Carl Mueller, Leonid Mytnik, Edwin C. Perkins
- 2015

We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P (0 < X(t, x) â‰¤ a) as a â†“ 0 as well as the Hausdorff dimension of the boundary of theâ€¦ (More)

- Carl Mueller, Leonid Mytnik, Edwin C. Perkins
- 2015

We study the density X(t, x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P (0 < X(t, x) â‰¤ a) as a â†“ 0 as well as the Hausdorff dimension of the boundary of theâ€¦ (More)

- EDWIN A. PERKINS, Edwin C. Perkins
- 2017

Â© Springer-Verlag, Berlin Heidelberg New York, 1983, tous droits rÃ©servÃ©s. Lâ€™accÃ¨s aux archives du sÃ©minaire de probabilitÃ©s (Strasbourg) (http://portail. mathdoc.fr/SemProba/) implique lâ€™accord avecâ€¦ (More)

- Carl Mueller, Leonid Mytnik, Edwin C. Perkins
- 2012

Motivated by Girsanovâ€™s nonuniqueness examples for SDEâ€™s, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) âˆ‚u âˆ‚t = âˆ† 2 u(t, x) + |u(t, x)|áº† (t, x), u(0, x) =â€¦ (More)