Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support
@article{Kliem2015TravellingWS, title={Travelling wave solutions to the KPP equation with branching noise arising from initial conditions with compact support}, author={Sandra Kliem}, journal={Stochastic Processes and their Applications}, year={2015}, volume={127}, pages={385-418} }
4 Citations
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References
SHOWING 1-10 OF 18 REFERENCES
Random Travelling Waves for the KPP Equation with Noise
- Mathematics
- 1995
Consider the stochastic partial differential equation [formula] where Ẇ =Ẇ(t, x) is two-parameter while noise. Assume that u0 is a continuous function taking values in [0, 1] such that for some…
A phase transition for a stochastic PDE related to the contact process
- Mathematics
- 1994
SummaryWe consider the one-dimensional heat equation, with a semilinear term and with a nonlinear white noise term. R. Durrett conjectured that this equation arises as a weak limit of the contact…
A travelling wave solution to the kolmogorov equation with noise
- Mathematics
- 1996
We consider the one-dimensional Kolmogorov equation driven by a particular space-time white noise term and show that there exist stochastic wavelike solutions which travel with a linear speed
TRANSIENCE, RECURRENCE AND LOCAL EXTINCTION PROPERTIES OF THE SUPPORT FOR SUPERCRITICAL FINITE MEASURE-VALUED DIFFUSIONS'
- Mathematics
- 1996
whose log-Laplace equation is associated with the semilinear equation Ut = Lu + flu - au2, where a,,8 > 0, and L = 1 Ed j= l aij (d92/( xXi dxj)) + Ed= 1 bi (d/8xi). A path X() is said to survive if…
Effect of noise on front propagation in reaction-diffusion equations of KPP type
- Mathematics
- 2009
AbstractWe consider reaction-diffusion equations of KPP type in one spatial dimension, perturbed by a Fisher-Wright white noise, under the assumption of uniqueness in distribution. Examples include…
Convergence of Rescaled Competing Species Processes to a Class of SPDEs
- Mathematics
- 2011
One can construct a sequence of rescaled perturbations of voter processes in dimension $d=1$ whose approximate densities are tight. By combining both long-range models and fixed kernel models in the…
Collision Local Times and Measure-Valued Processes
- MathematicsCanadian Journal of Mathematics
- 1991
Abstract We consider two independent Dawson-Watanabe super-Brownian motions, Y 1 and Y 2. These processes are diffusions taking values in the space of finite measures on ℝ d . We show that if d ≤ 5…
Super-Brownian motion: Path properties and hitting probabilities
- Mathematics
- 1989
SummarySample path properties of super-Brownian motion including a one-sided modulus of continuity and exact Hausdorff measure function of the range and closed support are obtained. Analytic…
Stochastic p.d.e.'s arising from the long range contact and long range voter processes
- Materials Science
- 1995
SummaryA long range contact process and a long range voter process are scaled so that the distance between sites decreases and the number of neighbors of each site increases. The approximate…