Long runs under a conditional limit distribution
Michel Broniatowski, Virgile Caron

TL;DR
This paper develops precise density approximations for long runs of a random walk conditioned on endpoint or average constraints, extending the Gibbs principle and enabling applications in rare event probability estimation and statistical inference.
Contribution
It introduces a sharp approximation method for the density of long conditioned random walk segments, extending the Gibbs conditional principle and providing tools for rare event analysis and inference.
Findings
Provides density approximations valid in large deviation regimes.
Extends Gibbs conditional principle to long subsequences.
Offers algorithms for simulation and approximation validity assessment.
Abstract
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the conditioning event it extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An approximation of the density of the runs is also obtained when the conditioning event states that the end value of the random walk belongs to a thin or a thick set with a nonempty interior. The approximations hold either in probability under the conditional distribution of the random walk, or in total variation norm between measures. An application of the approximation scheme to the evaluation of rare event probabilities through importance sampling is provided. When the conditioning event…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsProbability and Risk Models · Risk and Portfolio Optimization · Financial Risk and Volatility Modeling
