Related papers: Cost of diffusion: nonlinearity and giant fluctuat…
We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…
Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of…
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences.…
We study the propogation and diffusion of electric charge fluctuations in high energy heavy ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form…
Diffusivity is a key quantity in describing velocity fluctuations in granular materials. These fluctuations are the basis of many thermodynamic and hydrodynamic models which aim to provide a statistical description of granular systems. We…
We study a financial market where the risky asset is modelled by a geometric It\^o-L\'{e}vy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which…
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle…
Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to…
We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
In this paper,we consider a macro approximation of the flow of a risk reserve, The process is observed at discrete time points. Because we cannot directly observe each jump time and size then we will make use of a technique for identifying…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient…
Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved…
How much work does it cost for a propelled particle to stay localised near a stationary target, defying both thermal noise and a constant flow that would carry it away? We study the control of such a particle in finite time and find optimal…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…