Parameter Estimation in Stochastic Partial Differential Equations

Erscheinungsjahr 2027
ISBN: 978-3-032-39215-2
Verlag: Springer

Buch, Englisch, 502 Seiten, Format (B × H): 155 mm x 235 mm

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.

Zielgruppe

Research

Autoren/Hrsg.

Bishwal, Jaya P. N.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Hypothesis Testing for Fractional SPDE.- Quasi-likelihood Estimation in Fractional Levy SPDEs.- Conditional Least Squares Estimation in Nonlinear Fractional SPDEs.- Quasi-likelihood and Quasi-Bayes Estimation in Noncommutative Fractional SPDEs.- Approximate Maximum Likelihood Estimation in Semilinear SPDE.- Sieve Estimator for Fractional SPDEs.- 
Mixingale Estimation Function for Mixed Fractional SPDEs with Random Effect and Random Sampling.- Parameter Estimation in Fractional Stochastic Transport Equation.- Bayesian Inference for SPDEs with Small Noise.- Spectral Asymptotics of Bayes Estimators for SPDEs.- Inference for Stochastic Navier-Stokes Equation.

Über Autor(innen)

Dr. Jaya Bishwal is an Associate Professor of Mathematics and Statistics at the University of North Carolina at Charlotte, USA, where he serves as Chair of the Mathematical Finance Group. He is also the faculty advisor for the Theta Chapter of Pi Mu Epsilon, the national mathematics honor society.

An accomplished scholar and educator, Dr. Bishwal serves on the editorial boards of eight academic journals. He is the author of two books and has published 77 research articles in leading international refereed journals. In addition, he has reviewed manuscripts for 97 international journals, reflecting his extensive contributions to the academic community.

Dr. Bishwal’s research spans three broad areas: Mathematical Finance and Financial Engineering; Inference for Stochastic Processes and Financial Econometrics; and Mathematical Biology. His work has contributed significantly to the development of stochastic modeling, financial mathematics, and interdisciplinary applications of mathematics.

Over the past five years, he has taught advanced graduate-level courses, including and . Beyond his teaching and research responsibilities, Dr. Bishwal has held several important service roles within the university. He has chaired the Faculty Hiring Committee and served on the Graduate Curriculum Committee, Graduate Recruitment Committee, and Ph.D. Qualifying Examination Committee.

Through his scholarship, teaching, and leadership, Dr. Bishwal continues to advance research and education in mathematics, statistics, and quantitative finance.