Related papers: A System of Differential Equations for the Airy Pr…
We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for the number of such functionals. In contradiction to the common…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
We consider a system of differential equations the behavior of which solutions possesses several properties characteristic of the blood pressure distribution. The system can be used for a compartmental modeling of the cardiovascular system.…
For a class of particle systems in continuous space with local interactions, we show that the asymptotic diffusion matrix is an infinitely differentiable function of the density of particles. Our method allows us to identify relatively…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…
This paper reports on a new algorithm to compute the asymptotic solutions of a linear differential system. A feature of the algorithm is the ability to accommodate periodic coefficients.
We show that the supremum of the average of the Airy process and its time reversal minus a parabola is distributed as the maximum of two independent GUE Tracy-Widom random variables. The proof is obtained by considering a directed last…
The evaluation of the number of ways we can distribute energy among a collection of particles in a system is important in many branches of modern science. In particular, in multiparticle production processes the measurements of particle…
We prove some invariance principles for processes which generalize FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution. The limiting processes are extensions of the fractional L\'evy…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
We express the finite 3D Dimer partition function as a linear combination of determinants of oriented adjacency matrices, and the finite 3D Ising partition sum as a linear combination of products over aperiodic closed walks. The methodology…
Integral representations are considered of solutions of the inhomogeneous Airy differential equation $w''-z w=\pm1/\pi$. The solutions of these equations are also known as Scorer functions. Certain functional relations for these functions…
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
In this paper diffusion processes with changing modes are studied involving the variable order partial differential equations. We prove the existence and uniqueness theorem of a solution of the Cauchy problem for fractional variable order…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
The Ferrari-Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider $M$ such diffusions conditioned not to intersect. We show that the…
Various characterizations for fractional Levy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving Levy process, while others are in terms of differentiability properties of…