McKean, Jr.,
Diffusion processes and their sample paths, Springer, Berlin, 1974.
The jump distribution under the probability measure [Q.sup.*] is still a double exponential distribution with parameters [[eta].sup.*.sub.1] = [[eta].sub.1]-1, [[eta].sup.*.sub.2] = [[eta].sub.2] + 1, [p.sup.*] = (1/[omega])(p[[eta].sub.1]/ ([[eta].sub.1]-1), and [q.sup.*] = (1/[omega])(q[[eta].sub.2]/([[eta].sub.2] + 1)), which proves that the double exponential jump diffusion process under the measure transform is still a double exponential jump diffusion process; that is, both (31) and (35) are double exponential jump
diffusion processes. The Laplace transform of the first-passage time distribution of double exponential jump diffusion process has been obtained by Kou and Wang (2003) [26].
Pons explores tests of hypotheses in regular nonparametric models, including tests based on empirical processes and smooth estimators of density functions, regression functions, and regular functions defining the distribution of point processes and Gaussian
diffusion processes. He details the asymptotic behavior of the statistics and the asymptotic properties of the tests.
These results indicate that
diffusion processes are facilitated by longer shared tenure.
The confusion and
diffusion processes in cryptography proposed by Shannon [12] are applied in image encryption successfully.
The
diffusion processes as well as the produced models are described in the literature [3-8].
The various
diffusion processes have been studied in the literature, which are as follows.
For any multivariate Fokker-Planck equation there is an equivalent system of Ito
diffusion processes, such as the pair of (5)-(6)[12].
Particularly, through
diffusion processes have been carried out modeling interest rates and commodity prices, where they used in their modeling processes mean reversion.
On the background of above mentioned considerations can be concluded that the investigation of
diffusion processes on the air-water interface should be based on the classical theory of diffusion [19-22].
Specific questions addressed included: (1) What will a high-impact, technology-intensive STEM learning environment look like in the near and long-term future?; (2) What materials development and research are required to make this vision possible?; and (3) What design, development, and
diffusion processes are most likely to produce new approaches to STEM education?