We obtain a complete characterization of the quasi-stationary distributions of subcritical stable continuous-state branching processes in Brownian random environments, together with the domain of attraction of each member. These distributions form a one-parameter family whose modified Laplace transforms are given explicitly in terms of Tricomi's confluent hypergeometric function. For every initial distribution, we determine whether the conditional law converges to a QSD and identify that QSD whenever it does. The necessary and sufficient criteria are formulated in terms of the tail probabilities and moments of the initial law.
We study Brownian motion in R^d conditioned so that the time average of a continuous confining potential remains below a fixed level. On every fixed initial time interval, we prove that the conditioned process converges in total variation to the ground-state diffusion associated with a suitable Schr\"odinger operator....
In this paper, we focus on the asymptotic behavior of random iterated functions systems, in which both the family of transformations and the distribution of selecting them vary at each step. We consider two types of dynamics: the time-inhomogeneous Markov chain arising from forward iterates and the non-Markovian proces...
Abstract This paper investigates the impact of immigration with an infinite mean, driven by a discrete-stable compound Poisson process, on a critical branching environment with infinite variance of reproduction. Our objective is to derive an explicit expression for the probability generating function (p.g.f.) of the nu...
M. Slavtchova-Bojkova, Penka Mayster· Stochastics and Quality Cont...· 0 citations
We give a full characterization of the fixed points of Branching Brownian motion with critical and supercritical drifts under no additional assumptions besides it being locally finite almost surely. In particular, we do not assume finite intensity (Kabluchko, 2012) or the finite top particle (Chen-Garban-Shekhar, 2023)...
Xin-Xin Chen, Arnab Chowdhury, A. Shekhar et al.· 0 citations
We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an interface. If the jumps outside the membrane are i.i.d. mean-zero random variables with finite variance, then possible examples of the correspo...
A. Pilipenko· 0 citations
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