arXiv subjects

Eshwar R A

Publications and source records attributed to Eshwar R A.

3 recordsLinked to original sources

arXiv2026

Weak Form Recovery of Heston Type Stochastic Dynamics

Estimating the coupled drift, diffusion, and leverage structure of a stochastic-volatility model directly from a price path is an unresolved inverse problem: Kramers--Moyal increment estimators amplify sampling noise as the step shrinks, weak-form SINDy has not been extended to coupled two-dimensional diffusions or to the return--variance cross-variation producing leverage, and Heston calibration typically relies on option-implied surfaces rather than the physical-measure path. We extend the spatial weak-form Galerkin framework to the Heston model: variance increments, squared variance increments, squared price increments, and their cross-product are projected onto shared Gaussian kernels in variance space, giving one LASSO regression that jointly recovers mean reversion $κ$, long-run variance $θ$, vol-of-vol $ξ$, and leverage correlation $ρ$, with a drift-informed bias correction analogous to scalar-SDE diffusion debiasing. Across 30 daily-observed Heston simulations, $ξ$, $ρ$, and $ρξ$ are recovered with median errors under 2\%. Applied to S\&P 500 data spanning the 2007--2010 crisis, the method recovers negative leverage consistent with the documented equity leverage effect, and a 50-stock Indian panel shows the same sign under several independent variance proxies.

physics.data-an↗

arXiv2026

Symbolic Weak-form Recovery of 2-D Stochastic Generators

Recovering two-dimensional Ito generators from trajectory data is difficult because drift increments have low signal-to-noise, bivariate weak designs can be ill-conditioned, and unconstrained tensor estimates need not be positive semidefinite. We study WG-SINDy estimator combining covariance-shaped spatial kernels, a ridge-stabilized local-polynomial projection, adaptive-LASSO/STLSQ selection, one in-sample per-component feasible diagonal GLS pass, and a PSD projection--Cholesky read-out with mild isotropic shrinkage. The released estimator uses a data-dependent full-cloud smoother and one in-sample per-component feasible diagonal GLS pass; accordingly, we do not claim exact finite-sample martingale cancellation or a feasible-GLS efficiency theorem for the reported implementation. We evaluate the estimator on 29 synthetic two-dimensional systems: 19 meet their declared per-system recovery contracts, eight are retained as named limits, and two remain scoped reviews. Across the 19 PASS rows, the median central-grid drift metric is 0.204 and the median tensor error is 0.0397. Among the six systems with a finite, non-degenerate off-diagonal target, the median $a_{12}$ cosine is 0.997. Positive-semidefinite validity is imposed by construction. These results are synthetic, in-sample sampled-region diagnostics and do not establish universal or real-data recovery.

stat.ME↗

arXiv2026

Data-Driven Weak-form Discovery of Stochastic Systems

We present an algorithm for learning the governing equations of a stochastic dynamical system from trajectory data. It recovers interpretable symbolic expressions for both the drift $b(x)$ and the diffusion $a(x)$ in a single pass, yielding a model that can be queried directly for relaxation timescales, metastable escape rates, and stationary distributions. Rather than estimating the dynamics one time step at a time, the algorithm averages each candidate term across the whole trajectory before regressing; a drift-informed correction further removes the finite-sampling bias in the diffusion estimate, cutting it from 4.6% to 0.6% for state-dependent noise. We also show that the trajectory averaging must use a spatial rather than a temporal weighting: temporal weighting, as in existing weak-form methods, is biased for stochastic data with an error that grows with dataset size. On three benchmark systems -- the Ornstein--Uhlenbeck process, a double-well Langevin system, and a multiplicative-noise system -- the algorithm recovers all coefficients to within 5%, stationary densities to within 0.01 in total variation, and escape rates that match the true dynamics.

stat.ME↗