Related papers: Feynman-Kac particle integration with geometric in…
A discrete-time end-to-end fiber-optical channel model is derived based on the first-order perturbation approach. The model relates the discrete-time input symbol sequences of co-propagating wavelength channels to the received symbol…
In this work a Feynman-Kac path integral method based on Levy measure has been proposed for solving the Cauchy problems associated with the space-time fractional Schroedinger equations arising in interacting systems in fractional quantum…
In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive…
The persistent walk is a classical model in kinetic theory, which has also been studied as a toy model for MCMC questions. Its continuous limit, the telegraph process, has recently been extended to various velocity jump processes (Bouncy…
Multi-agent systems can be successfully described by kinetic models, which allow one to explore the large scale aggregate trends resulting from elementary microscopic interactions. The latter may be formalised as collision-like rules, in…
We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…
We investigate a chain of oscillators with anharmonic on-site potentials, with long range interparticle interactions, and coupled both to external and internal stochastic thermal reservoirs of Ornstein-Uhlenbeck type. We develop an integral…
Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that…
The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
We study large deviations principles for $ N $ random processes on the lattice $ \Z^d $ with finite time horizon $ [0,\beta] $ under a symmetrised measure where all initial and terminal points are uniformly given by a random permutation.…
We study deterministic discrete time exclusion type spatially heterogeneous particle processes in continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
Diffusion models for continuous state spaces based on Gaussian noising processes are now relatively well understood from both practical and theoretical perspectives. In contrast, results for diffusion models on discrete state spaces remain…
Understanding the non-equilibrium dynamics of extended quantum systems after the trigger of a sudden, global perturbation (quench) represents a daunting challenge, especially in the presence of interactions. The main difficulties stem from…
Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
The main results of this paper comprise proofs of the following two related facts: (i) the Feynman--Kac formula is a functor $F_*$, namely, between a stochastic differential equation and a dynamical system on a statistical manifold, and…