Diffusion Approximations of Branching Processes
نویسندگان
چکیده
منابع مشابه
On Local Linear Approximations to Diffusion Processes
Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hen...
متن کاملSimple Binomial Processes as Diffusion Approximations in Financial Models
A binomial approximation to a diffusion is defined as “computationally simple” if the number of nodes grows at most linearly in the number of time intervals. It is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models. The convergence of the sequence of bond and European option prices from these processes to the...
متن کاملDiffusion Approximations
In this chapter, we shall give an overview of some of the basic applications of the theory of diffusion approximations to operations research. A diffusion approximation is a technique in which a complicated and analytically intractable stochastic process is replaced by an appropriate diffusion process. A diffusion process is a (strong) Markov process having continuous sample paths. Diffusion pr...
متن کاملBranching Processes
Galton-Watson processes were introduced by Francis Galton in 1889 as a simple mathematical model for the propagation of family names. They were reinvented by Leo Szilard in the late 1930s as models for the proliferation of free neutrons in a nuclear fission reaction. Generalizations of the extinction probability formulas that we shall derive below played a role in the calculation of the critica...
متن کاملBranching Processes
The study of branching processes began in the 1840s with Irénée-Jules Bienaymé, a probabilist and statistician, and was advanced in the 1870s with the work of Reverend Henry William Watson, a clergyman and mathematician, and Francis Galton, a biometrician. In 1873, Galton sent a problem to the Educational Times regarding the survival of family names. When he did not receive a satisfactory answe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1971
ISSN: 0003-4851
DOI: 10.1214/aoms/1177693076