Lower deviation probabilities for supercritical Galton–Watson processes
On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case
Under a well-known scaling, supercritical Galton–Watson processes converge to a non-degenerate non-negative random limit variable . We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent lower deviation...
Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst.
Conditional limit theorems for ordered random walks.
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