相关论文: Representations of the finite-dimensional point de…
We show that if drift coefficients of Arratia flows converge in $L_1(R)$ or $L_{\infty}(R)$ then the 1-point densities associated with these flows converge to the density for the flow with the limit drift.
In the paper we consider the point measure that corresponds to Arratia flow. The central limit theorem of the multiple integrals with respect to this measure was obtained.
The rate of the weak convergence in the fractional step method for the Arratia flow is established in terms of the Wasserstein distance between the images of the Lebesque measure under the action of the flow. We introduce finite-dimensional…
This work is devoted to long-time properties of the Arratia flow with drift -- a stochastic flow on $\mathbb{R}$ whose one-point motions are weak solutions to a stochastic differential equation $dX(t)=a(X(t))dt+dw(t)$ that move…
An analog of the Trotter formula for the Arratia flow is presented. Perturbations of the Brownian web by mappings associated with an ordinary differential equation with a smooth right part are considered and proved to be convergent…
Given two stochastic equations with different drift terms, under very weak assumptions Liptser and Shiryaev provide the equivalence of the laws of the solutions to these equations by means of Girsanov transform. Their assumptions involve…
We construct a modified Arratia flow with mass and energy conservation. We suppose that particles have a mass obeying the conservation law, and their diffusion is inversely proportional to the mass. Our main result asserts that such a…
The weak limits of the measure-valued processes organized as a mass carried by the interacting Brownian particles are described. As a limiting flow the Arrattia flow is obtained.
The article contains description of the functionals from the family of coalescing Brownian particles. New type of the stochastic integral is introduced and used.
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…
A kind of Pettis integral representation for a Banach valued It\^o process is given and its drift term is modified using a Girsanov Theorem.
For a class of coalescing stochastic flows on the real line the existence of dual flows is proved. A stochastic flow and its dual are constructed as a forward and backward perfect cocycles over the same metric dynamical system. The metric…
We consider discrete porous medium equations of the form \partial_t \rho_t = \Delta \phi(\rho_t), where \Delta is the generator of a reversible continuous time Markov chain on a finite set X, and \phi is an increasing function. We show that…
In this paper we have constructed an approximation for the Harris flow and the Arratia flow using a sequence of independent stationary Gaussian processes as a perturbation. We have established what should be the relationship between the…
The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of…
The purpose of this note is to give an example of stochastic flows of kernels, which naturally interpolates between the Arratia coalescing flow associated with systems of coalescing independent Brownian particles on the circle and the…
The structure of square integrable functionals measurable with respect to the $n-$point motion of the Arratia flow is studied. Relying on the change of measure technique, a new construction of multiple stochastic integrals along…
Stochastic flows generated by reflected SDEs in a half-plane with an additive diffusion term are considered. A derivative in the initial data is represented a.s. as an infinite product of matrices. We use this representation and construct…
In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point…
Extending previous work [arXiv:1408.0628] by the first author we present a variant of the Arratia flow, which consists of a collection of coalescing Brownian motions starting from every point of the unit interval. The important new feature…