1 edition of **A diffusion approximation analysis of a general n-compartment system** found in the catalog.

A diffusion approximation analysis of a general n-compartment system

Donald Paul Gaver

- 155 Want to read
- 5 Currently reading

Published
**1977**
by Naval Postgraduate School in Monterey, Calif
.

Written in English

- Compartmental analysis (Biology),
- Diffusion processes,
- Stochastic differential equations,
- Mathematical models

A new approach to the stochastic analysis of general compartment models is presented. The analysis is based on the concept of diffusion approximations. The state of a compartment system is represented as the superposition of a deterministic process, characterized by a system of ordinary differential equations, and a random noise process characterized by stochastic differential equations. All transition rate parameters are permitted to be time dependent. Numerical solutions are presented for the two-compartment case. Extensions to non-linear compartment models are discussed.

**Edition Notes**

Statement | by Donald P. Gaver and John P. Lehoczky |

Contributions | Lehoczky, John P., Naval Postgraduate School (U.S.) |

The Physical Object | |
---|---|

Pagination | 41 p. ; |

Number of Pages | 41 |

ID Numbers | |

Open Library | OL25528572M |

A diffusion approximation for limit order book models. which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized t: Titel changed, appendix added, presentation improve This paper derives a diffusion approximation for a. In this paper, the reliability of the two methods from the family of fourth-order implicit finite difference schemes, namely the fourth-order Crank-Nicolson approximation scheme and the fourth-order standard implicit approximation scheme in solving the diffusion equation has been studied.

Accuracy of the Diffusion Approximation. The original description of the Diffusion Approximation (DA), in its general form for a multiple (more than 2) state Markov Chain (MC), implies the calculation of the square root of a matrix,. As this is too time consuming to be performed in real time, the uncoupled particles approximation, consisting. This book provides recent results on the stochastic approximation of systems by weak convergence techniques. General and particular schemes of proofs for average, diffusion, and Poisson approximations of stochastic systems are presented, allowing one to simplify complex systems and obtain numerically tractable models.

THE GENERAL SOLUTION. A general n-compartment system is determined by n 2 parameters, i.e., n turnover rates and n(n − 1) transfer rates. The transfer function of such a system contains n coefficients in the numerator and n in the denominator. When n > 2, the solution of such system is undetermined, and it contains n(n − 2. During the week of October ,, Northwestern University hosted an international conference on the theme "Diffusion Processes and Related Problems in Analysis." This was attended by partici pants representing 14 different countries. The conference, which is part of the "Emphasis Year".

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