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Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\theta$ of physical significance which…
In this paper, we study the relation between the smallest $g$-supersolution of constraint backward stochastic differential equation and viscosity solution of constraint semilineare parabolic PDE, i.e. variation inequalities. And we get an…
We propose a probabilistic numerical algorithm to solve Backward Stochastic Differential Equations (BSDEs) with nonnegative jumps, a class of BSDEs introduced in [9] for representing fully nonlinear HJB equations. In particular, this allows…
We present a new algorithms to discretize a decoupled forward backward stochastic differential equations driven by pure jump L\'evy process (FBSDEL in short). The method is built in two steps. Firstly, we approximate the FBSDEL by a forward…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our…
For given computational resources, the accuracy of plasma simulations using particles is mainly held back by the noise due to limited statistical sampling in the reconstruction of the particle distribution function. A method based on…
In a Markovian framework, we consider the problem of finding the minimal initial value of a controlled process allowing to reach a stochastic target with a given level of expected loss. This question arises typically in approximate hedging…
Local volatility is an important quantity in option pricing, portfolio hedging, and risk management. It is not directly observable from the market; hence calibrations of local volatility models are necessary using observable market data.…
The strong relative arbitrage problem in Stochastic Portfolio Theory seeks an investment strategy that almost surely outperforms a benchmark portfolio at the end of a given time horizon. The highest relative return in relative arbitrage…
When a posterior peaks in unexpected regions of parameter space, new physics has either been discovered, or a bias has not been identified yet. To tell these two cases apart is of paramount importance. We therefore present a method to…
In this paper, we present a backward deep BSDE method applied to Forward Backward Stochastic Differential Equations (FBSDE) with given terminal condition at maturity that time-steps the BSDE backwards. We present an application of this…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…
We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also…
We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter $H\in(0,1)$. Close to a change of stability measured with a small parameter $\varepsilon$, we rely on the natural…
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given…
The estimation of non-Gaussian measurement noise models is a significant challenge across various fields. In practical applications, it often faces challenges due to the large number of parameters and high computational complexity. This…
In this paper, we study the prediction of a circularly symmetric zero-mean stationary Gaussian process from a window of observations consisting of finitely many samples. This is a prevalent problem in a wide range of applications in…
We consider a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution…