Titlebook: Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications; Johan Grasman,Onno A. Herwaarden Book 1999 Springe

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舊石器時(shí)代

極大的痛苦

J. W. Bakker,W. P. Roever,G. Rozenberg pumping well. For the study of groundwater pollution it is not sufficient to model the transport of particles by advection only. In addition the mechanism of macroscopic dispersion has to be taken in consideration. It accounts for the random motion of individual particles in the flow. In this study

Protein

Essentials of Object-Oriented Programming,imensional systems: a prey-predator system and the epidemiological problem of contact between infectives and susceptibles. The method we use is rather complex. It is for that reason that we do not expect that the method will be taken over by population biologists. In Sect. 7.3 we show how the proble

Pandemic

Essentials of Object-Oriented Programming,resents the “ideal” state of the system. Due to the stochastic perturbations the system fluctuates about this equilibrium state. In order to quantify the functioning of the system we introduce concepts as confidence domain and return time. A confidence domain in state space is a bounded domain conta

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Dynamical Systems Perturbed by Noise: the Langevin Equation in different fields of applications, such as in stochastic mechanics and in the dynamics of biological populations. Depending on the application, the noise may have quite different origins. Outside fluctuations affecting a physical system can be incorporated in the modelling in the form of a stocha

驚奇

Singular Perturbation Analysis of the Differential Equations for the Exit Probability and Exit Time ation method. However, in some of these problems the standard method fails and we have to introduce more refined methods such as the WKB-method or a variational approach. Of course we may as well produce an exact solution and make an asymptotic approximation with the Laplace method applied to this e

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The Fokker—Planck Equation in Several Dimensions: the Asymptotic Exit Probleming. The situation that a part of the boundary is reflecting or not attainable will arise in some special problems. The case that both the drift and normal component of the diffusion vanish at the boundary will be examined in Chap. 7. The latter is of special importance in the field of stochastic dy