Related papers: Importance sampling for jump processes and applica…
The normalizing constant plays an important role in Bayesian computation, and there is a large literature on methods for computing or approximating normalizing constants that cannot be evaluated in closed form. When the normalizing constant…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requiring the evaluation of the second derivative of the potential in addition…
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented…
Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst…
We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…
This work explores the nature of augmented importance sampling in safety-constrained model predictive control problems. When operating in a constrained environment, sampling based model predictive control and motion planning typically…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
Importance sampling is a popular variance reduction method for Monte Carlo estimation, where a notorious question is how to design good proposal distributions. While in most cases optimal (zero-variance) estimators are theoretically…
We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…
In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…
Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted…
This article investigates discrete-time approximations of stochastic integrals driven by semimartingales with jumps via weighted bounded mean oscillation (BMO) approach. This approach enables $L_p$-estimates, $p \in (2, \infty)$, for the…
Diffusion models are an important tool for generative modelling, serving as effective priors in applications such as imaging and protein design. A key challenge in applying diffusion models for downstream tasks is efficiently sampling from…
We study large deviation principles for Gaussian processes lifted to the free nilpotent group of step N. We apply this to a large class of Gaussian processes lifted to geometric rough paths. A large deviation principle for enhanced…
The reliability of a complex industrial system can rarely be assessed analytically. As system failure is often a rare event, crude Monte-Carlo methods are prohibitively expensive from a computational point of view. In order to reduce…
We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into…
In the need for low assumption inferential methods in infinite-dimensional settings, Bayesian adaptive estimation via a prior distribution that does not depend on the regularity of the function to be estimated nor on the sample size is…
The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical…
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…