 By David Machin (auth.)

Best stochastic modeling books

Stochastic partial differential equations with Levy noise: An evolution equation approach

Contemporary years have obvious an explosion of curiosity in stochastic partial differential equations the place the riding noise is discontinuous. during this finished monograph, major specialists element the evolution equation method of their answer. lots of the effects seem the following for the 1st time in booklet shape, and the amount is certain to stimulate additional examine during this very important box.

Discrete stochastic processes

Stochastic strategies are present in probabilistic structures that evolve with time. Discrete stochastic techniques swap by means of in basic terms integer time steps (for it slow scale), or are characterised through discrete occurrences at arbitrary occasions. Discrete Stochastic techniques is helping the reader enhance the knowledge and instinct essential to follow stochastic approach concept in engineering, technological know-how and operations examine.

Mathematical Statistics and Stochastic Processes

Ordinarily, books on mathematical data are limited to the case of self reliant identically dispensed random variables. during this ebook even though, either this situation AND the case of established variables, i. e. facts for discrete and non-stop time tactics, are studied. This moment case is essential for today’s practitioners.

Extra info for Biomathematics: An Introduction

Sample text

4. Expand (1 + 2/v)v as a binomial series and hence, by letting v be very large, show that lim v-+oo [1 + -vz)v 22 23 = 1 + 2 +-- +-- + ... 2! 3! What is the corresponding series for ~ vr 1 (1 + 2 5. A statistical distribution of great importance in many branches of biology, especially ecology, is the Poisson distribution whose successive terms are where r = 0, 1, 2, ••• oo and,\> 0. , r=O . 1 . ) ( Note: 6. Evaluate the terms of the binomial expansion of (1/2 + 1/2) 4 • Check that the terms sum to unity.

Calculate the population size after 5 generations on the following assumptions: (a) each mother cell continues to produce daughters; (b) the mother cell fails to produce daughters after the first division but nevertheless survives; (c) the mother cell produces daughters for two generations and then herself dies. (9) The total length (tip of snout to notch of flukes) and length from tip of snout to blowhole of seven adult male Humpback whales (Megaptera novaeangliae) are given in the following table.

7, which is taken from Bliss (1970, page 244). This shows that the mean of the square root of the number of normal human births in each hour of the day in a certain hospital is well fitted by a sine curve. 18) where t is the time in hours on a 24 hour clock (end of interval) and y is the mean square-root number of births. 18 is t (time) and not an angle. However, if we think of 24 hours as one complete cycle then 24 hours is equivalent to 2rr radians. Thus t = 0 corresponds to 8 = 0, t = 1 corresponds to 8 = 2rr/24 radians and so on.