Related papers: Branching-stable point processes
Branching processes are a class of continuous-time Markov chains (CTMCs) prevalent for modeling stochastic population dynamics in ecology, biology, epidemiology, and many other fields. The transient or finite-time behavior of these systems…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
In the paper we consider a stochastic model which called Markov Q-processes that forms a continuous-time Markov population system. Markov Q-processes are defined as stochastic Markov branching processes with trajectories continuing in the…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under…
We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifractional $\alpha$-stable processes, and multistable processes,…
In this paper we focus on the pathwise stability of mild solutions for a class of stochastic partial differential equations which are driven by switching-diffusion processes with jumps. In comparison to the existing literature, we show…
The normalised partial sums of values of a nonnegative multiplicative function over divisors with appropriately restricted sizes of a random permutation from the symmetric group define trajectories of a stochastic process. We prove a…
We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton--Watson processes. The class includes as specific cases the…
We study the convergence of random function iterations for finding an invariant measure of the corresponding Markov operator. We call the problem of finding such an invariant measure the stochastic fixed point problem. This generalizes…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring…
Timesteppers constitute a powerful tool in modern computational science and engineering. Although they are typically used to advance the system forward in time, they can also be viewed as nonlinear mappings that implicitly encode steady…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
It has long been known that complex balanced mass-action systems exhibit a restrictive form of behaviour known as locally stable dynamics. This means that within each compatibility class $\mathcal{C}_{\mathbf{x}_0}$---the forward invariant…
We consider the problem of quantifying and assessing the steady-state voltage stability in radial distribution networks. Our approach to the voltage stability problem is based on a local, approximate, and yet highly accurate…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
A stochastic model is presented for a super-position of uncorrelated pulses with a random distribution of amplitudes, sizes, velocities and arrival times. The pulses are assumed to move radially with fixed shape and amplitudes decaying…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…