Related papers: The maximal jump and local convergence of continuo…
We study the height of the maximal particle at time $t$ of a one dimensional branching Brownian motion with a space-dependent branching rate. The branching rate is set to zero in finitely many intervals (obstacles) of order $t$. We obtain…
Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric L\'evy processes are studied. The L\'evy measure is assumed to…
Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a L\'evy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In…
The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…
In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions to SDE's. We formulate conditions ensuring existence and uniqueness in law of solutions. We investigate Markov property. To…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…
In this paper, we consider a class of generalized continuous-state branching processes obtained by Lamperti type time changes of spectrally positive L\'evy processes using different rate functions. When explosion occurs to such a process,…
New results on conditional joint probability distributions of first exit times are presented for a continuous-time stochastic process defined as the mixture of Markov jump processes moving at different speeds on the same finite state space,…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Let $(Z_n)$ be a supercritical branching process in a random environment $\xi$. We study the convergence rates of the martingale $W_n = Z_n/ E[Z_n| \xi]$ to its limit $W$. The following results about the convergence almost sur (a.s.), in…
It is common practice to treat small jumps of L\'evy processes as Wiener noise and thus to approximate its marginals by a Gaussian distribution. However, results that allow to quantify the goodness of this approximation according to a given…
The aim of this paper is two-fold. First we analyze the sequence of intensity measures of a spatial branching point process arising in a multiple target tracking context. We study its stability properties, characterize its long time…
We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substantially weaker assumptions than known in the literature. In…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
We call a random point measure infinitely ramified if for every $n\in \mathbb N$, it has the same distribution as the $n$-th generation of some branching random walk. On the other hand, branching L\'evy processes model the evolution of a…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
The maximum likelihood state for a simplified stochastic thermohaline circulation model is investigated. It is shown that a jump occurs for the maximum likelihood state during transitions between two metastable states. The jump helps to…
We study the problem of optimal stopping of conditional McKean-Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean-Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a…
We present an elementary state augmentation method for a class of static risk measure applied to the total cost for both Markov decision processes and stochastic optimal control, such that dynamic programming equations can be derived on the…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…