Local extinction versus local exponential growth for spatial branching processes

By János Engländer, Andreas E. Kyprianou. 2004

109 citations recorded by the source corpus.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a82d1fe7ad0f69e86166afb10b56883b822ffdb2

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, methodology): “For example, the principal eigenvalue is used to characterise the stability of equilibrium of a reaction-diffusion equation enabling the definition of persistence criteria [18, 19, 20, 5, 33, 44, 53].”
Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation: one sided travelling-waves (2006, background): “For a detailed setup and notation for these changes of measure and spine decompositions in branching Brownian motion the reader should refer to the recent new approach presented in Hardy and Harris [17], in addition to Kyprianou [27] and Chauvin and Rouault [9].”
Travelling wave solutions to the K-P-P equation: alternatives to Simon Harris' probabilistic analysis (2004, methodology): “The methods used here to deduce martingale convergence have also been used successfully in [20] for related martingales that appear naturally for more general branchingMarkov diffusions.”
Martingales and Profile of Binary Search Trees (2004, unknown): “For the underlying branching random walk this construction is classical [3],[14],[20],.”
Liouville-type results for semilinear elliptic equations in unbounded domains (2007, background): “For special nonlinearities of the type f (x, u) = b(x)u−a(x)u2, with inf a > 0, this existence result is due to Engländer and Pinsky (see [10], and also [9], [13]).”
Multifractal spectra and precise rates of decay in homogeneous fragmentations (2006, methodology): “This is used in Section 4 to derive some limit theorems which may be of independent interest (see Engländer and Kyprianou [14] for a related approach in the setting of spatial branching processes).”
On the principal eigenvalue of elliptic operators in $\R^N$ and applications (2006, unknown): “In [10], Engl ä der and Pinsky proved a similar existence result for a class of solutions of minimal growth (which they define there) for nonlinearities of the type f (x, u) = b(x)u− a(x)u2 with inf a > 0 (see also [9], [22]).”