In these lectures, we give an account of certain recent developments of the theory of spatial
branching processes. These developments lead to several fas cinating probabilistic objects …

The parameter estimation theory for stochastic differential equations driven by Brownian
motions or general Lévy processes with finite second moments has been well developed. In …

This monograph presents some new concentration inequalities for Feynman-Kac particle
processes. We analyze different types of stochastic particle models, including particle profile …

Consider a countable collection of particles located on a countable group, performing a
critical branching random walk where the branching rate of a particle is given by a random …

We develop a general probabilistic approach that enables one to get sharp estimates for the
almost-sure short-term behavior of hierarchically structured branching-diffusion processes …

We delineate a connection between the stochastic evolution of the cluster structure of a
specific branching–diffusing particle system and a certain previously unknown structure …

The two-level superprocess arises as the high-density diffusion limit of a two-level branching
Brownian motion, in which particles are grouped into superparticles in which they …

We derive different local approximations along with estimates of the remainders for the total
mass processes of two branching particle systems. To this end, we investigate the …

We prove local limit theorems for the total mass processes of two branchingfluctuating
particle systems which converge to discontinuous (2, d, β)-superprocess. To this end, we …