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Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…
This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living,…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and…
In this contribution, a stochastic theory for a branching process in a neutron population with two energy levels is investigated. In particular, a variance to mean or Feynman-alpha formula is derived in this generalized scenario using the…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We…
The approximation of the Feynman-Kac semigroups by systems of interacting particles is a very active research field, with applications in many different areas. In this paper, we study the parallelization of such approximations. The total…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…
Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Inhomogeneous models of populations and communities allow for birth and death rates to vary among…
Extensive cooperation among unrelated individuals is unique to humans, who often sacrifice personal benefits for the common good and work together to achieve what they are unable to execute alone. The evolutionary success of our species is…
We propose a Bayesian nonparametric approach to modelling and predicting a class of functional time series with application to energy markets, based on fully observed, noise-free functional data. Traders in such contexts conceive profitable…
The ubiquity of multiscale interactions in complex systems is well-recognized, with development and heredity serving as a prime example of how processes at different temporal scales influence one another. This work introduces a novel…