Exact simulation of diffusion first exit times: algorithm acceleration
Authors: Samuel Herrmann, Cristina Zucca
JMLR 2022 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The efficiency of this acceleration is pointed out through numerical examples. Keywords: Exit time, Brownian motion, diffusion processes, rejection sampling, exact simulation, multi-armed bandit, randomized algorithm. ... Finally, in the last section we illustrate the efficiency of this new algorithm considering classical diffusion processes like the Ornstein-Uhlenbeck process or the Cox-Ingersoll-Ross model. |
| Researcher Affiliation | Academia | Samuel Herrmann EMAIL Institut de Math ematiques de Bourgogne (IMB) UMR 5584, CNRS, Universit e de Bourgogne Franche-Comt e F-21000 Dijon, FRANCE; Cristina Zucca EMAIL Department of Mathematics G. Peano University of Torino, Via Carlo Alberto 10 10123 Turin, ITALY |
| Pseudocode | Yes | Algorithm 1: Box Exit(x, [l, u], T) ... Algorithm 2: Diffusion Exit Problem Diff Exit(T, N) ... Algorithm 3: Bandit Diff Exit(T, N0) |
| Open Source Code | Yes | The open-source code corresponding to the C++ programs used in Section 4 is available at https://github.com/Sam Herr/Diff-First Exit Time-Acceleration |
| Open Datasets | No | The paper focuses on simulating first exit times for diffusion processes using mathematical models and internal simulations, such as 'Example 1: The diffusion process with unitary diffusion coefficient and with the following drift term: µ0(x) = 2+sin(x)' and 'Ornstein-Uhlenbeck process' or 'Cox-Ingersoll-Ross Processes'. It does not use or provide access information for any external, publicly available datasets. |
| Dataset Splits | No | The paper describes simulation experiments where 'sample size' (e.g., 'sample of size 10 000') refers to the number of generated simulated instances for evaluating algorithm performance. It does not utilize or specify any training/test/validation splits of an external dataset. |
| Hardware Specification | Yes | All the numerical tests have been done on the same computer: Intel Core i5, 1.6 GHz |
| Software Dependencies | No | The paper mentions that the code is implemented in 'C++ programs' and provides a GitHub link, but it does not specify version numbers for the C++ compiler or any libraries used, which are required for a reproducible software description. |
| Experiment Setup | Yes | Example 1: The diffusion process with unitary diffusion coefficient and with the following drift term: µ0(x) = 2+sin(x). We consider the exit problem from the interval [a, b] = [0, 7], the diffusion starting in x = 3. ... Data: x (starting position), T, N0, γ( ) and β( ) (input functions), M (size of the sample: number of simulations), ϵ (parameter in the ϵ-greedy algorithm). ... Here N is chosen in the set {2, . . . , 21} accordingly to the ϵ-greedy algorithm with ϵ = 0.1, and the average is computed using a sample of size 10 000. |