Related papers: Introduction to SPDEs from Probability and PDE

The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& R\"ockner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math.\ Soc.] has turned out to be a useful instrument to study…

These notes provide a short, focused introduction to modelling stochastic gene expression, including a derivation of the master equation, the recovery of deterministic dynamics, birth-and-death processes, and Langevin theory. The notes were…

We study a generalization of the Monge--Kantorovich optimal transport problem. Given a prescribed family of time-dependent probability measures $(\mu_t)$, we aim to find, among all path-continuous stochastic processes whose one-dimensional…

This is the write-up of the talk I gave at the 23rd International Symposium on Mathematical Programming (ISMP) in Bordeaux, France, July 6th, 2018. The talk was a general overview of the state of the art of time-varying, mainly convex,…

Probability estimation is essential for every statistical data compression algorithm. In practice probability estimation should be adaptive, recent observations should receive a higher weight than older observations. We present a…

We consider the Cauchy problem for a linear stochastic partial differential equation. By extending the parametrix method for PDEs whose coefficients are only measurable with respect to the time variable, we prove existence, regularity in…

In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in…

We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive L\'{e}vy noise. The main result is applicable to various types of…

This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…

These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for…

This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…

This paper investigates a Stochastic Partial Differential Equation (SPDE) derived from the Fokker-Planck equation associated with Score-based Generative Models. We modify the standard Fokker-Planck equation to better represent practical…

Time-to-event models are a popular tool to analyse data where the outcome variable is the time to the occurrence of a specific event of interest. Here we focus on the analysis of time-to-event outcomes that are either intrisically discrete…

Using a combination of recurrent neural networks and signature methods from the rough paths theory we design efficient algorithms for solving parametric families of path dependent partial differential equations (PPDEs) that arise in pricing…

These are lecture notes from a course offered at the Bangalore School on Statistical Physics - X, during 17-28 June 2019, [ https://www.icts.res.in/program/bssp2019 ] at International centre of theoretical physics (ICTS), Bangalore. These…

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

These lecture notes are based on lectures given in 2019 Saint-Flour Probability School.

This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…

These are the lecture notes for a course on exceptional polynomials taught at the \textit{AIMS-Volkswagen Stiftung Workshop on Introduction to Orthogonal Polynomials and Applications} that took place in Douala (Cameroon) from October 5-12,…

We present a comprehensive computational study of the short-time transport properties of bidisperse neutral colloidal suspensions and the corresponding porous media. Our study covers bidisperse particle size ratios up to $4$, and total…