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Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.

Distribution (Probability theory) --- Mathematical statistics. --- Mathematics. --- Numerical analysis. --- Math --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Distribution functions --- Frequency distribution --- Statistical methods --- Mathematical analysis. --- Analysis (Mathematics). --- Game theory. --- Economics, Mathematical. --- Probabilities. --- Statistics. --- Analysis. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Statistical Theory and Methods. --- Numerical Analysis. --- Game Theory, Economics, Social and Behav. Sciences. --- Mathematical analysis --- Science --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Games, Theory of --- Theory of games --- Mathematical models --- 517.1 Mathematical analysis --- Methodology --- Statistics --- Probabilities --- Sampling (Statistics) --- Characteristic functions --- Global analysis (Mathematics). --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Currency question --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Economics, Mathematical . --- Statistics . --- Parameter estimation. --- Stochastic differential equations --- Statistical methods. --- Differential equations --- Fokker-Planck equation --- Estimation theory --- Stochastic systems

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This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Mathematical statistics --- statistiek --- Parameter estimation. --- Stochastic differential equations. --- Estimació d'un paràmetre --- Equacions diferencials estocàstiques

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• Reference Manager
• EndNote
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Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modelling complex phenomena and making beautiful decisions. The subject has attracted researchers from several areas of mathematics and other related fields like economics and finance. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods. Useful because of the current availability of high frequency data is the study of refined asymptotic properties of several estimators when the observation time length is large and the observation time interval is small. Also space time white noise driven models, useful for spatial data, and more sophisticated non-Markovian and non-semimartingale models like fractional diffusions that model the long memory phenomena are examined in this volume.

Statistical science --- Operational research. Game theory --- Numerical analysis --- stochastische analyse --- speltheorie --- kansrekening --- numerieke analyse --- statistisch onderzoek