Related papers: A diffusion approximation for limit order book mod…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
We present a numerical approximation method for linear diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known…
In this paper, we consider modeling time-dependent multi-server queues that include abandonments and retrials. For the performance analysis of those, fluid and diffusion models called "strong approximations" have been widely used in the…
As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…
Focusing on hybrid diffusion dynamics involving continuous dynamics as well as discrete events, this article investigates the explicit approximations for nonlinear switching diffusion systems modulated by a Markov chain. Different kinds of…
In this paper, we propose an approach for computing invariant sets of discrete-time nonlinear systems by lifting the nonlinear dynamics into a higher dimensional linear model. In particular, we focus on the \emph{maximal admissible…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded…
The main objective of the present paper is to construct a new class of space-time discretizations for the stochastic $p$-Stokes system and analyze its stability and convergence properties. We derive regularity results for the approximation…
Given a discounted cost, we study deterministic discrete-time systems whose inputs are generated by policy iteration (PI). We provide novel near-optimality and stability properties, while allowing for non stabilizing initial policies. That…
Discrete diffusion models form a powerful class of generative models across diverse domains, including text and graphs. However, existing approaches face fundamental limitations. Masked diffusion models suffer from irreversible errors due…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
Shadow systems are an approximation of reaction-diffusion-type problems obtained in the infinite diffusion coefficient limit. They allow reducing complexity of the system and hence facilitate its analysis. The quality of approximation can…
We consider a perturbed ordinary differential equation where the perturbation is only significant when a one-dimensional null recurrent diffusion is close to zero. We investigate the first order correction to the unperturbed system and…
We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…
An interpolation method for discretising continuous-time Linear Time Invariant (LTI) models is proposed in this paper. It consists first in using the Loewner interpolation framework on a specific set of frequency data and secondly to…
The study of minimax convergence rates for classification procedures adapted to SDE paths is rarely addressed in the literature. Only one paper established optimal convergence rates for a binary classifier for SDE paths constructed from the…