Generator Identification for Linear SDEs with Additive and Multiplicative Noise

• URL: http://arxiv.org/abs/2310.19491v2
• Date: Sun, 21 Jan 2024 22:35:34 GMT
• Title: Generator Identification for Linear SDEs with Additive and Multiplicative Noise
• Authors: Yuanyuan Wang, Xi Geng, Wei Huang, Biwei Huang, Mingming Gong
• Abstract summary: identifiability conditions are crucial in causal inference using linear SDEs. We derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise. We offer geometric interpretations of the derived identifiability conditions to enhance their understanding.
• Score: 48.437815378088466
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings.

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