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Cascades of Poisson processes are probabilistic models for spatio-temporal phenomena in which (i) previous events may trigger subsequent events, and (ii) both the background and triggering processes are conditionally Poisson. Such phenomena…

Multi-particle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three non-equilibrium…

Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a…

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale…

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…

This paper analyses a system subject to multiple dependent degradation processes. Degradation processes start at random times following a non homogeneous Poisson process and next dependently propagate. The growth of these degradation…

In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…

In this paper, we consider an extension of the Poisson random measure for the formulation of continuous-time reinforcement learning, such that both the frequency and the width of the jumps depend on the path. Starting from a general point…

Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…

In supervised learning, we fit a single statistical model to a given data set, assuming that the data is associated with a singular task, which yields well-tuned models for specific use, but does not adapt well to new contexts. By contrast,…

In this paper, we model dependence between operational risks by allowing risk profiles to evolve stochastically in time and to be dependent. This allows for a flexible correlation structure where the dependence between frequencies of…

By using coupling by change of conditional probability measure, the log-Harnack inequality for path dependent McKean-Vlasov SDEs with distribution dependent diffusion coefficients is established, which together with the exponential…

Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…

We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…

We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distribution and Poisson distribution of order k. An explicit…

One of the challenges in using numerical methods to address many-body problems is the multi-dimensional integration over poles. More often that not, one needs such integrations to be evaluated as a function of an external variable. An…

Markov decision processes (MDPs) are used to model a wide variety of applications ranging from game playing over robotics to finance. Their optimal policy typically maximizes the expected sum of rewards given at each step of the decision…

These lecture notes aim at a post-Bachelor audience with a background at an introductory level in Applied Mathematics and Applied Statistics. They discuss the logic and methodology of the Bayes-Laplace approach to inductive statistical…