The extremal process of two-speed branching Brownian motion
By Anton Bovier, Lisa Hartung. 2013
57 citations recorded by the source corpus.
We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $\sigma_1$ for $s\leq bt$ and $\sigma_2$ when $bt\leq s\leq t$. In the case $\sigma_1>\sigma_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $\sigma_1<\sigma_2$, a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of Arguin, Bovier, and Kistler.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c4a0824d4f592da864f7660bc6055dd508ecc10b
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Citations in the corpus
- Freezing and Decorated Poisson Point Processes (2014, methodology): “SDPPP in BBM, two-speed BBM and BRW.”
- Extrema of log-correlated random variables: Principles and Examples (2016, background): “odels. The study of such types of models go back to Derrida who introduced the Generalized Random Energy Models [31]. In the case of BRW, these are called time-inhomogeneous BRW. They were studied in [21,22,36,37,52]. A similar scale-inhomogenous eld for the Gaussian free eld was introduced and stud”
- Branching random walks (2015, background): “For the study of extremes in models with a timeinhomogeneous branching mechanism, see Fang and Zeitouni [108]–[109], Maillard and Zeitouni [187], Mallein [188]–[189], Bovier and Hartung [63]–[64].”