Related papers: Simulation de trajectoires de processus continus

In this paper the computational aspects of probability calculations for dynamical partial sum expressions are discussed. Such dynamical partial sum expressions have many important applications, and examples are provided in the fields of…

Road user trajectory prediction in dynamic environments is a challenging but crucial task for various applications, such as autonomous driving. One of the main challenges in this domain is the multimodal nature of future trajectories…

Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…

Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…

Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…

We propose a hybrid deterministic and stochastic approach to achieve extended time scales in atomistic simulations that combines the strengths of molecular dynamics (MD) and Monte Carlo (MC) simulations in an easy-to-implement way. The…

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…

In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of…

Demand for high-performance, robust, and safe autonomous systems has grown substantially in recent years. These objectives motivate the desire for efficient safety-theoretic reasoning that can be embedded in core decision-making tasks such…

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

This paper gives a brief overview on the nonparametric techniques that are useful for financial econometric problems. The problems include estimation and inferences of instantaneous returns and volatility functions of time-homogeneous and…

The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…

In this paper we present a framework for risk-sensitive model predictive control (MPC) of linear systems affected by stochastic multiplicative uncertainty. Our key innovation is to consider a time-consistent, dynamic risk evaluation of the…

These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…

Renewable energy projects, such as large offshore wind farms, are critical to achieving low-emission targets set by governments. Stochastic computer models allow us to explore future scenarios to aid decision making whilst considering the…

Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…

Diffusion models, which leverage stochastic processes to capture complex data distributions effectively, have shown their performance as generative models, achieving notable success in image-related tasks through iterative denoising…

Because the stochastic calculus yields rarely random variables with laws defined by explicit closed formulas, probabilistic numerical computations are done most often by simulation. The simulation by the shift, whose field of application is…

In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…