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O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

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Variational approach to rare event simulation using least-squares regression.

Carsten Hartmann¹, Omar Kebiri¹, Lara Neureither¹

¹Institute of Mathematics, Brandenburgische Technische Universität Cottbus-Senftenberg, 03046 Cottbus, Germany.

Chaos (Woodbury, N.Y.)

|July 4, 2019

Summary

We developed an adaptive importance sampling method for simulating rare events in diffusion processes. This zero-variance technique optimizes the change of measure by reformulating it as a stochastic control problem, improving simulation efficiency.

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Area of Science:

Computational Physics
Stochastic Processes
Numerical Analysis

Background:

Simulating rare events in diffusion processes is computationally challenging.
Existing methods often lack efficiency for high-dimensional problems.

Purpose of the Study:

To introduce an adaptive importance sampling scheme for efficient rare event simulation.
To optimize the change of measure for zero-variance estimation.

Main Methods:

Utilizing a Gibbs variational principle to determine the optimal change of measure.
Reformulating the problem as a stochastic optimal control problem.
Solving the control problem via stochastic approximation and Feynman-Kac representation.

Main Results:

The proposed scheme offers an efficient approach for rare event simulation.
The method is applicable to diffusion processes.
Numerical aspects for high-dimensional problems are discussed.

Conclusions:

The adaptive importance sampling scheme provides a robust and efficient method for rare event simulation.
The connection to stochastic optimal control offers a novel solution pathway.