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We consider the stochastic Allen--Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$, and study the semidiscretisation in time of the equation by an Euler type split-step…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
The ionized interstellar medium disperses pulsar radio signals, resulting in a stochastic time-variable delay known as the dispersion measure (DM) noise. In the wideband paradigm of pulsar timing, we measure a DM together with a time of…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
In recent years, instanton calculus has successfully been employed to estimate tail probabilities of rare events in various stochastic dynamical systems. Without further corrections, however, these estimates can only capture the exponential…
This paper introduces an online approach for identifying time-varying subspaces defined by linear dynamical systems. The approach of representing linear systems by non-parametric subspace models has received significant interest in the…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
We show that multiscaling properties of developed turbulence in shell models, which lead to anomalous scaling exponents in the inertial range, are determined exclusively by instanton dynamics. Instantons represent correlated extreme events…
By optimal fluctuation method, we study short-time distribution $P(\mathcal{A}=A)$ of the functionals, $\mathcal{A}=\int_{0}^{t_f} x^n(t) dt$, along constrained trajectories of random acceleration process for a given time duration $t_f$,…
The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
The validity of the instanton analysis approach is tested numerically in the case of the diffraction-amplification problem $\partial_z\psi -\frac{i}{2m}\partial^2_{x^2} \psi =g\vert S\vert^2\, \psi$ for $\ln U\gg 1$, where…
Guided diffusion sampling relies on approximating often intractable likelihood scores, which introduces significant noise into the sampling dynamics. We propose using adaptive moment estimation to stabilize these noisy likelihood scores…
A typical audio signal processing pipeline includes multiple disjoint analysis stages, including calculation of a time-frequency representation followed by spectrogram-based feature analysis. We show how time-frequency analysis and…
In this paper, we focus on non-asymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative diffusion term (non-constant diffusion coefficient). More precisely, the objective of this paper is to…
The identification of anomalies is a critical component of operating complex, and possibly large-scale and geo-graphically distributed cyber-physical systems. While designing anomaly detectors, it is common to assume Gaussian noise models…
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…
We analyse the convergence and stability of a micro-macro acceleration algorithm for Monte Carlo simulations of stiff stochastic differential equations with a time-scale separation between the fast evolution of the individual stochastic…