相关论文: On time dynamics of coagulation-fragmentation proc…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
In this note we consider the Glauber dynamics for the mean-field Ising model, when all couplings are equal and the external field is uniform. It is proved that the relaxation time of the dynamics is monotonically decreasing in temperature.
We discuss relaxation and aging processes in the one- and two-dimensional $ABC$ models. In these driven diffusive systems of three particle types, biased exchanges in one direction yield a coarsening process characterized in the long time…
In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…
Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed,…
Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and…
We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily…
We study ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching. The first set of results concerns the ergodic properties of the properly scaled joint Markov process with a parameter that…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
Time-dependent correlation functions of (unstable) particles undergoing biased or unbiased diffusion, coagulation and annihilation are calculated. This is achieved by similarity transformations between different stochastic models and…
The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…
We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…
This paper investigates the model for pedestrian flow firstly proposed in [Cristiani et al., DOI:10.1137/140962413]. The model assumes that each individual in the crowd moves in a known domain, aiming at minimizing a given cost functional.…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge…
Realistic description of patient-specific mechanical properties of clotting dynamics presents a major challenge. Available patient-specific data falls short of robustly characterizing myriads of complex dynamic interactions that happen…
We study the generalized Forchheimer flows of slightly compressible fluids in heterogeneous porous media. The media's porosity and coefficients of the Forchheimer equation are functions of the spatial variables. The partial differential…
We propose a novel family of entanglement measures for time-separated subsystems. Our definitions are applicable to any quantum system, continuous or discrete. To illustrate their utility, we derive upper and lower bounds on time-separated…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…