Related papers: A Method to Calculate the Exit Time in Stochastic …

This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…

In line with the methodology introduced in our recent article for formulating probabilistic representations of integration by parts involving killed diffusion, we establish an integration by parts formula for the first exit time of…

We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…

In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction.…

This paper considers the problem of minimizing the time average of a controlled stochastic process subject to multiple time average constraints on other related processes. The probability distribution of the random events in the system is…

In scheduling problems, deterministic task durations are often assumed. This usually does not capture reality and may lead to schedules that are not robust to (small) changes to these task lengths. The use of stochastic task durations…

The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…

Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and…

Numerical simulation codes are very common tools to study complex phenomena, but they are often time-consuming and considered as black boxes. For some statistical studies (e.g. asset management, sensitivity analysis) or optimization…

The increasing application of cardiorespiratory simulations for diagnosis and surgical planning necessitates the development of computational methods significantly faster than the current technology. To achieve this objective, we leverage…

We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…

Stochastic simulators are an indispensable tool in many branches of science. Often based on first principles, they deliver a series of samples whose distribution implicitly defines a probability measure to describe the phenomena of…

Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…

In this study, we have developed a parallel version of the random time simulation algorithm. Firstly, we gave a rigorous basis of the random time description of the stochastic process of chemical reaction network time evolution. And then we…

Controlling complex dynamical systems has been a topic of considerable interest in academic circles in recent decades. While existing works have primarily focused on closed-loop control schemes with infinite-time durations, this paper…

As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also…

The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still…

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation…

Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…

We analyze the finite sample regret of a decreasing step size stochastic gradient algorithm. We assume correlated noise and use a perturbed Lyapunov function as a systematic approach for the analysis. Finally we analyze the escape time of…