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6 papers · 2 filters
Time-Homogeneous Diffusions with a Given Marginal at a Random Time
Alexander M. G. Cox, David G. Hobson, Jan K. Obłój
We solve explicitly the following problem: for a given probability measure mu, we specify a generalised martingale diffusion X which, stopped at an independent exponential time T,…
Traveling waves and homogeneous fragmentation
J. Berestycki, S. C. Harris, A. E. Kyprianou
We formulate the notion of the classical Fisher-Kolmogorov-Petrovskii-Piscounov (FKPP) reaction diffusion equation associated with a homogeneous conservative fragmentation process…
Further calculations for the McKean stochastic game for a spectrally negative Levy process: from a point to an interval
Erik J. Baurdoux, Kees van Schaik
Following Baurdoux and Kyprianou [2] we consider the McKean stochastic game, a game version of the McKean optimal stopping problem (American put), driven by a spectrally negative L…
Approaching criticality via the zero dissipation limit in the abelian avalanche model
Antal A. Járai, Frank Redig, Ellen Saada
The discrete height abelian sandpile model was introduced by Bak, Tang & Wiesenfeld and Dhar as an example for the concept of self-organized criticality. When the model is modified…
Smoothness of scale functions for spectrally negative Levy processes
Terence Chan, Andreas Kyprianou, Mladen Savov
Scale functions play a central role in the fluctuation theory of spectrally negative Lévy processes and often appear in the context of martingale relations. These relations are oft…
Limit theorems for random spatial drainage networks
Mathew D. Penrose, Andrew R. Wade
Suppose that under the action of gravity, liquid drains through the unit -cube via a minimal-length network of channels constrained to pass through random sites and to flow with…