Related papers: On continuous state branching processes: condition…

Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…

Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a…

In this note, we study the asymptotic behaviour near extinction of (sub-) critical continuous state branching processes. In particular, we establish an analogue of Khintchin's law of the iterated logarithm near extinction time for a…

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…

We consider continuous state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term extinction and explosion behaviours…

A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The extinction and explosion probabilities and the mean extinction and…

A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…

In this paper, we obtain a Lamperti type representation for real-valued self-similar Markov processes, killed at their hitting time of zero. Namely, we represent real-valued self-similar Markov processes as time changed multiplicative…

Ba\~nuelos and Bogdan (2004) and Bogdan, Palmowski and Wang (2016) analyse the asymptotic tail distribution of the first time a stable (L\'evy) process in dimension $d\geq 2$ exists a cone. We use these results to develop the notion of a…

We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…

For a positive self-similar Markov process, X, we construct a local time for the random set, $\Theta$, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its…

We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…

We present a new approach to positive self-similar Markov processes (pssMps) by reformulating Lamperti's transformation via jump type SDEs. As applications, we give direct constructions of pssMps (re)started continuously at zero if the…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…

In this work we give a complete description to the asymptotic behaviors of exponential functionals of L\'evy processes and divide them into five different types according to their convergence rates. Not only their exact convergence speeds…

Motivated by the stochastic Lotka-Volterra model, we introduce discrete-state interacting multitype branching processes. We show that they can be obtained as the sum of a multidimensional random walk with a Lamperti-type change proportional…

Branching processes and Fleming-Viot processes are two main models in stochastic population theory. Incorporating an immigration in both models, we generalize the results of Shiga (1990) and Birkner et al. (2005) which respectively connect…

Let $(X_n)_{n\ge 1}$ be a Markov chain on a measurable state space $X$, and let $S_n = \sum_{k=1}^n f(X_k)$ be the associated Markov walk. For $y>0$, denote by $\tau_y$ the first time at which $y+S_n$ becomes non-positive. Assuming that the…

We consider fragmentation processes with values in the space of marked partitions of $\mathbb{N}$, i.e. partitions where each block is decorated with a nonnegative real number. Assuming that the marks on distinct blocks evolve as…