Parameter Estimation in Stochastic Partial Differential Equations - Jaya P. N. Bishwal

Stochastic partial differential equations (SPDEs) provide a powerful framework for modeling space-time phenomena influenced by randomness, with applications ranging from finance and neuroscience to fluid dynamics and cell biology. While the analytical theory of SPDEs is well established, statistical inference for these models remains a rapidly developing area.

This book presents a comprehensive treatment of parameter estimation and hypothesis testing for SPDEs, covering likelihood, quasi-likelihood, Bayesian, minimum contrast, sieve, and sequential methods under both continuous and discrete observations, including random sampling schemes. It addresses linear and nonlinear models, fractional and Lévy-driven SPDEs, stochastic transport equations, Navier-Stokes equations, interacting particle systems, and biological applications.

Bringing together recent advances and original developments, this volume serves as a valuable reference for researchers and graduate students working in stochastic analysis, statistics, mathematical finance, econometrics, and applied mathematics.