Parameter Estimation In Stochastic Differential Equations
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Author | : Jaya P. N. Bishwal |
Publisher | : Springer |
Total Pages | : 271 |
Release | : 2007-09-26 |
Genre | : Mathematics |
ISBN | : 3540744487 |
Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. 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.
Author | : Simo Särkkä |
Publisher | : Cambridge University Press |
Total Pages | : 327 |
Release | : 2019-05-02 |
Genre | : Business & Economics |
ISBN | : 1316510085 |
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author | : Marianne Huebner |
Publisher | : |
Total Pages | : 248 |
Release | : 1993 |
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Author | : Jaya P. N. Bishwal |
Publisher | : Springer Nature |
Total Pages | : 634 |
Release | : 2022-08-06 |
Genre | : Mathematics |
ISBN | : 3031038614 |
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.
Author | : |
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Total Pages | : 16 |
Release | : 2005 |
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Author | : Kęstutis Kubilius |
Publisher | : Springer |
Total Pages | : 403 |
Release | : 2018-01-04 |
Genre | : Mathematics |
ISBN | : 3319710303 |
This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.
Author | : Rong SITU |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2006-05-06 |
Genre | : Technology & Engineering |
ISBN | : 0387251758 |
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Author | : Yu. A. Kutoyants |
Publisher | : |
Total Pages | : 224 |
Release | : 1984 |
Genre | : Parameter estimation |
ISBN | : |
Author | : Raphael Abel Kasonga |
Publisher | : National Library of Canada |
Total Pages | : 190 |
Release | : 1986 |
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Author | : Mathieu Kessler |
Publisher | : CRC Press |
Total Pages | : 509 |
Release | : 2012-05-17 |
Genre | : Mathematics |
ISBN | : 1439849404 |
The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a spectrum of estimation methods, including nonparametric estimation as well as parametric estimation based on likelihood methods, estimating functions, and simulation techniques. Two chapters are devoted to high-frequency data. Multivariate models are also considered, including partially observed systems, asynchronous sampling, tests for simultaneous jumps, and multiscale diffusions. Statistical Methods for Stochastic Differential Equations is useful to the theoretical statistician and the probabilist who works in or intends to work in the field, as well as to the applied statistician or financial econometrician who needs the methods to analyze biological or financial time series.