CLT Variance Associated with Baxendale's SDE
Steven R. Finch
TL;DR
This paper analyzes the variance of the Central Limit Theorem related to Baxendale's stochastic differential equation, providing insights into eigenvalues of Ince's equation and verifying results numerically.
Contribution
It offers a novel analysis of the CLT variance in Baxendale's SDE and connects it to eigenvalues of Ince's equation, addressing an open problem.
Findings
Eigenvalue analysis clarifies CLT variance behavior.
Numerical verification supports theoretical results.
Provides new insights into stochastic Lyapunov exponents.
Abstract
Simple analysis of the leftmost eigenvalue of Ince's equation (a boundary value problem with periodicity) resolves an open issue surrounding a stochastic Lyapunov exponent. Numerical verification is also provided.
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Taxonomy
Topicsstochastic dynamics and bifurcation · Stochastic processes and financial applications · Spectral Theory in Mathematical Physics