8 papers
On the local well-posedness of randomly forced reaction-diffusion equations with initial data and a superlinear reaction term
Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart
We consider a parabolic stochastic partial differential equation (SPDE) on that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusio…
Fast convergence rates for estimating the stationary density in SDEs driven by a fractional Brownian motion with semi-contractive drift
Chiara Amorino, Eulalia Nualart, Fabien Panloup +1
We study the estimation of the invariant density of additive fractional stochastic differential equations with Hurst parameter . We first focus on continuous observati…
Convergence of continuous-time stochastic gradient descent with applications to deep neural networks
Gabor Lugosi, Eulalia Nualart
We study a continuous-time approximation of the stochastic gradient descent process for minimizing the population expected loss in learning problems. The main results establish gen…
On the well-posedness of SPDEs with locally Lipschitz coefficients
Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart
We consider the stochastic partial differential equation, where is defined for $(t\,,x)\in(0\,,\infty)…
On the implied volatility of Inverse options under stochastic volatility models
Elisa Alòs, Eulalia Nualart, Makar Pravosud
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a gener…
Differential Machine Learning for Time Series Prediction
Akash Yadav, Eulalia Nualart
Accurate time series prediction is challenging due to the inherent nonlinearity and sensitivity to initial conditions. We propose a novel approach that enhances neural network pred…