Delay-coordinate reconstruction and conditional-moment causal diagnostics in stochastic systems
Partial observation and delay-coordinate reconstruction are rooted in deterministic dynamical-systems theory, whereas there are many systems with intrinsic stochasticity. We propose a conditional-moment interpretation of delay-coordinate reconstruction for stochastic systems, in which a delay vector is used to reconstruct conditional moments of a future distribution rather than a unique future sample path. Two complementary arguments motivate this viewpoint. First, the probability density of a stochastic differential equation obeys a deterministic Fokker-Planck equation and, under certain assumptions, is represented by an infinite deterministic hierarchy of moments. Hence, a finite-moment...
| Authors | Jun Ohkubo |
|---|---|
| Primary category | cs.LG |
| Published | 4 October 2026 |
| Last updated at source | 4 October 2026 |
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