by American Mathematical Society .
Written in English
|The Physical Object|
|Number of Pages||216|
Describes the asymptotic methods for parameter estimation and hypothesis testing based on asymptotic properties of the likelihood ratios in the case where an observed stochastic process is a This English edition includes an extensive list of references and revised bibliographical notes. A maximal inequality and tightness for multiparameter stochastic processes (B.G. Ivanoff, N.C. Weber). Part 8: Results related to studies of local time and hitting times of Bessel processes, a cautionary note on limiting sigma-algebras. On asymptotic independence of partial sums (E. Csáki, A. Földes).Book Edition: 1. Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and robustness, second-order processes in discrete and continuous time and diffusion processes Cited by: 7. She is currently a professor at Taras Shevchenko National University of Kyiv. She is the author/coauthor of more than research papers and 9 books. Her research interests include theory and statistics of stochastic processes, stochastic differential equations, fractional processes, stochastic analysis, and financial mathematics.
Vo/, Stochastic processes I: Asymptotic behat•iour and symmetries it starts at the value mathematical conditions that there exists a unique solution for an honest conditional probability f R(xt I ys) dx = 1, for all t, s;t > s, () which satisfies both the forward and backward equation, are discusSed for time. Statistical Inference for Stochastic Processes Theory and Methods. Book • It also discusses some results on estimation of marginal density for stationary Markov processes and stationary mixing processes. The asymptotic results for density estimation in general for dependent observations are essentially the same as those in the case. Statistical Inference Stochastic Processes provides information pertinent to the theory of stochastic processes. This book discusses stochastic models that are increasingly used in scientific research and describes some of their applications. Organized into three parts encompassing 12 chapters, this book begins with an overview of the basic. ASYMPTOTIC THEORY OF CERTAIN "GOODNESS OF FIT" CRITERIA BASED ON STOCHASTIC PROCESSES Columbia University and University of Michigan 1. Summary. The statistical problem treated is that of testing the hypothesis that n independent, identically distributed random variables have a specified continuous distribution function F(x).
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today’s practitioners. Mathematical Statistics and Stochastic Processes is based. It proposes the term “statistical methods mining” to describe the process of applying (and describing the location of one's research within) the virtual encyclopedia of statistical knowledge. It proposes to publicize research by using various frameworks and maps of the world of statistical knowledge. This book is suitable as a professional reference book on statistical anal ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes. 2 ESTIMATING FUNCTIONS FOR DIFFUSION-TYPE PROCESSES Xn∆ is the one-dimensional stochastic differential equation dXt = −θtan(Xt)dt+ dWt, where θ>0 and Wis a Wiener process. The state-space is(−π/2,π/2). This model will be considered in more detail in Subsection For this process Kessler & Sørensen () proposed the estimating.