Related papers: Variational Inference for L\'evy Process-Driven SD…

L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…

Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of L\'evy…

Modeling uncertainty in heavy-tailed time series remains a critical challenge for deep probabilistic forecasting models, which often struggle to capture abrupt, extreme events. While L\'evy stable distributions offer a natural framework for…

Pure-jump L\'evy processes are popular classes of stochastic processes which have found many applications in finance, statistics or machine learning. In this paper, we propose a novel family of self-decomposable L\'evy processes where one…

Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…

We introduce L\'evy-Flows, a class of normalizing flow models that replace the standard Gaussian base distribution with L\'evy process-based distributions, specifically Variance Gamma (VG) and Normal-Inverse Gaussian (NIG). These…

In this article we consider parametric Bayesian inference for stochastic differential equations (SDE) driven by a pure-jump stable Levy process, which is observed at high frequency. In most cases of practical interest, the likelihood…

We consider the problem of obtaining effective representations for the solutions of linear, vector-valued stochastic differential equations (SDEs) driven by non-Gaussian pure-jump L\'evy processes, and we show how such representations lead…

In this paper we introduce a new class of state space models based on shot-noise simulation representations of non-Gaussian L\'evy-driven linear systems, represented as stochastic differential equations. In particular a conditionally…

Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps.…

Financial returns are known to exhibit heavy tails, volatility clustering and abrupt jumps that are poorly captured by classical diffusion models. Advances in machine learning have enabled highly flexible functional forms for conditional…

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions…

We obtain sample-path large deviations for a class of one-dimensional stochastic differential equations with bounded drifts and heavy-tailed L\'evy processes. These heavy-tailed L\'evy processes do not satisfy the exponential integrability…

Generating accurate extremes from an observational data set is crucial when seeking to estimate risks associated with the occurrence of future extremes which could be larger than those already observed. Applications range from the…

In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for…

We introduce and analyze multilevel Monte Carlo algorithms for the computation of $\mathbb {E}f(Y)$, where $Y=(Y_t)_{t\in[0,1]}$ is the solution of a multidimensional L\'{e}vy-driven stochastic differential equation and $f$ is a real-valued…

In this paper we consider Bayesian parameter inference associated to a class of partially observed stochastic differential equations (SDE) driven by jump processes. Such type of models can be routinely found in applications, of which we…

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…

Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…

Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…