Related papers: From CKLS Process to CIR-type and OU-type Processe…
In this paper, we address high-dimensional parametric estimation of the drift function in diffusion models, specifically focusing on a $d$-dimensional ergodic diffusion process observed at discrete time points. We consider both a general…
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…
We consider a pure-jump stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) process driven by a non-symmetric stable L{\'e}vy process with jump activity $\alpha$ $\in$ (1, 2) and we address the joint estimation of drift, scaling and jump…
Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian. Observations using purely long distance…
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with…
I investigate the Kazakov-Migdal (KM) model -- the Hermitean gauge-invariant matrix model on a D-dimensional lattice. I utilize an exact large-N solution of the KM model with a logarithmic potential to examine its critical behavior. I find…
We propose a change detection method for the famous Cox--Ingersoll--Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one- and two-sided…
We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate $\Gamma_{\textrm{CS}}$ divided by the product of the entropy density $s$ and temperature $T$ behaves across different kinds of phase transitions in the…
We consider the minor process of (Hermitian) matrix diffusions with constant diagonal drifts. At any given time, this process is determinantal and we provide an explicit expression for its correlation kernel. This is a measure on the…
We present a unified framework to efficiently approximate solutions to fractional diffusion problems of stationary and parabolic type. After discretization, we can take the point of view that the solution is obtained by a matrix-vector…
We present first elements of an extension of Yakhot's model of strong turbulence towards small scales. The analysis is based on an empirically observed relation for even order structure functions which extends from the inertial into the…
In this paper, we establish new quantitative convergence bounds for a class of functional autoregressive models in weighted total variation metrics. To derive our results, we show that under mild assumptions, explicit minorization and…
In this paper, we prove pathwise uniqueness for stochastic systems of McKean-Vlasov type with singular drift, even in the measure argument, and uniformly non-degenerate Lipschitz diffusion matrix. Our proof is based on Zvonkin's…
In this paper we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a…
This paper discusses model order reduction of large sparse second-order index-3 differential algebraic equations (DAEs) by applying Iterative Rational Krylov Algorithm (IRKA). In general, such DAEs arise in constraint mechanics, multibody…
Motivated by a probabilistic approach to Kahler-Einstein metrics we consider a general non-equilibrium statistical mechanics model in Euclidean space consisting of the stochastic gradient flow of a given (possibly singular) quasi-convex…
We present an effective field theory for a unified description of transport in normal and superconducting metals in the presence of generic spin-orbit coupling (SOC). The structure of the quantum kinetic theory in the diffusive regime is…
A general method is proposed which allows one to estimate drift and diffusion coefficients of a stochastic process governed by a Langevin equation. It extends a previously devised approach [R. Friedrich et al., Physics Letters A 271, 217…
Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…