Search results for "stochastic"

Noise effect in a sine-Gordon Lattice

2013

International audience; This paper is devoted to the influence of internal noise in a sine-Gordon chain exhibiting the well known nonlinear supratransmission phenomenon. It is shown that spatiotemporal noise can trigger breather modes with a given probability in a range of parameters where they do not occur without noise. A frequency analysis is carried out to quantify the degree of coherence of the emitted breather. It is shown that there exists an appropriate amount of noise which ensures the existence of breather modes with the best coherence.

Inference of proto-neutron star properties from gravitational-wave data in core-collapse supernovae

2021

The eventual detection of gravitational waves from core-collapse supernovae (CCSN) will help improve our current understanding of the explosion mechanism of massive stars. The stochastic nature of the late post-bounce gravitational wave signal due to the non-linear dynamics of the matter involved and the large number of degrees of freedom of the phenomenon make the source parameter inference problem very challenging. In this paper we take a step towards that goal and present a parameter estimation approach which is based on the gravitational waves associated with oscillations of proto-neutron stars (PNS). Numerical simulations of CCSN have shown that buoyancy-driven g-modes are responsible …

Ghost stochastic resonance in FitzHugh–Nagumo circuit

2014

International audience; The response of a neural circuit submitted to a bi-chromatic stimulus and corrupted by noise is investigated. In the presence of noise, when the spike firing of the circuit is analysed, a frequency not present at the circuit input appears. For a given range of noise intensities, it is shown that this ghost frequency is almost exclusively present in the interspike interval distribution. This phenomenon is for the first time shown experimentally in a FitzHugh-Nagumo circuit.

Gradient and Lipschitz Estimates for Tug-of-War Type Games

2021

We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed

On the local and global regularity of tug-of-war games

2018

This thesis studies local and global regularity properties of a stochastic two-player zero-sum game called tug-of-war. In particular, we study value functions of the game locally as well as globally, that is, close to the boundaries of the game domains. Furthermore, we formulate a continuous time stochastic differential game and discuss, among other things, the equicontinuity of the families of value functions. The main motivation is to understand the properties of the games on their own right. As applications, we obtain an existence and a regularity result for a nonlinear elliptic p-Laplace type partial differential equation and a characterization of the solution to a parabolic p-Laplace typ…

Gradient walks and $p$-harmonic functions

2017

Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities

2018

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.

Approximation of heat equation and backward SDEs using random walk : convergence rates

2018

This thesis addresses questions related to approximation arising from the fields of stochastic analysis and partial differential equations. Theoretical results regarding convergence rates are obtained by using discretization schemes where the limiting process, the Brownian motion, is approximated by a simple discrete-time random walk. The rate of convergence is derived for a finite-difference approximation of the solution of a terminal value problem for the backward heat equation. This weak approximation result is proved for a terminal function which has bounded variation on compact sets. The sharpness of the according rate is achieved by applying some new results related to the first exit time …

Regularity properties of tug-of-war games and normalized equations

2017

Stochastic fracture analysis of systems with moving material

2015

This paper considers the probability of fracture in a system in which a material travels supported by rollers. The moving material is subjected to longitudinal tension for which deterministic and stochastic models are studied. In the stochastic model, the tension is described by a multi-dimensional Ornstein-Uhlenbeck process. The material is assumed to have initial cracks perpendicular to the travelling direction, and a stochastic counting process describes the occurrence of cracks in the longitudinal direction of the material. The material is modelled as isotropic and elastic, and LEFM is applied. For a general counting process, when there is no fluctuation in tension, the reliability of t…