Computing expected values of functions involving extreme values of diffusion processes can find many applications in financial engineering.
Right column: the image fusion of the ADCdiff maps of co-transplanted tumours reveals the existence of extreme values of diffusion (red = high; dark blue = low).
Snieder et al. (2007) showed that the Green's function can be retrieved from the response to random forcing for a variety of conditions, including the extreme case of the diffusion equation.
Combined with the importance sampling technique and the Williams path decomposition of Brownian motion, this approach transforms simulating extreme values of a general diffusion process to simulating two Brownian meanders.
"However, it gives a good indication as far as the two most extreme models are concerned, with demic diffusion (expanding farmers) on one side and a strict cultural diffusion (transfer of ideas) on the other".
To the extremes of these ranges for diffusion and degradation, the oscillatory amplitude varies and synchrony is not completely perfect.
Introducing membrane diffusion prevented the more extreme polarization states from being reached and reduced the number of steady-states.
Initially, four alternative extreme scenarios were simulated: DD/gcc: Demic diffusion with gene-culture coevolution hypothesis; the frequency of LC T*Pis transmitted from one population to the next (Figure 1 and Figure S1) along the presumed route of Neolithic diffusion assuming a migration of people spreading their know-how.
This technique overcomes the extreme difficulties of determining effective diffusivities of the products under reaction conditions in pellet diffusion cells.
Our numerical results were found to be in excellent agreement with those of the Lifshitz Slyozov Wagner (LSW) theory for the asymptotic behavior of the system for the extreme cases of reaction- and diffusion-limited nanoparticle growth, thus establishing the validity of the algorithm.
