Related papers: Sample path properties of the stochastic flows
We consider a stochastic flow $\phi_t(x,\omega)$ in $\mathbb{R}^n$ with initial point $\phi_0(x,\omega)=x$, driven by a single $n$-dimensional Brownian motion, and with an outward radial drift of magnitude $\frac{…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
We consider a stochastic flow on $\mathds{R}$ generated by an SDE with its drift being a function of bounded variation. We show that the flow is differentiable with respect to the initial conditions. Asymptotic properties of the flow are…
The article shows a bridge representation for the joint density of a system of stochastic processes consisting of a Brownian motion with drift coupled with a correlated fractional Brownian motion with drift. As a result, a small time…
In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is…
We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. A general framework is constructed to make precise the notions of…
Non-typical transport phenomena may arise when randomly driven particles remain in an active relationship with the environment instead of being passive. If we attribute to Brownian particles an ability to induce alterations of the…
In this paper we establish limit theorems for power variations of stochastic processes controlled by fractional Brownian motions with Hurst parameter $H\leq 1/2$. We show that the power variations of such processes can be decomposed into…
A 2D Stochastic incompressible non-Newtonian fluids driven by fractional Bronwnian motion with Hurst parameter $H \in (1/2,1)$ is studied. The Wiener-type stochastic integrals are introduced for infinite-dimensional fractional Brownian…
We introduce a technique to merge two biased Brownian motions into a single regular process. The outcome follows a stochastic differential equation with a constant diffusion coefficient and a non-linear drift. The emerging stochastic…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional and the rates are equal to the…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
We prove the central limit theorem of random variables induced by distances to Brownian paths and Green functions on the universal cover of Riemannian manifolds of finite volume with pinched negative curvature. We further provide some…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
We investigate Gibbs measures relative to Brownian motion in the case when the interaction energy is given by a double stochastic integral. In the case when the double stochastic integral is originating from the Pauli-Fierz model in…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
We consider the stochastic continuity equation driven by Brownian motion. We use the techniques of the Malliavin calculus to show that the law of the solution has a density with respect to the Lebesgue measure. We also prove that the…
We analyze the steady-state flow as a function of the initial density for a class of deterministic cellular automata rules (``traffic rules'') with periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1 (1998)]. We…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…