Learning Controlled Stochastic Differential Equations

תקציר מקורי באנגליתarXiv:2411.01982v2 Announce Type: replace-cross Abstract: We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values. From trajectory data, we aim to estimate coefficients whose induced density flows reproduce those of the observed dynamics. The data consist of several controls sampled from a finite-dimensional family and, for each control, multiple independent trajectories observed at discrete times over a fixed horizon. The controls are observed inputs, not learner-selected decisions. We propose a kernel method for multidimensional nonlinear controlled SDEs. The method estimates the density flow for each sampled control, then f