## Stochastic Population Processes: Analysis, Approximations, SimulationsThe vast majority of random processes in the real world have no memory - the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive event-time pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation |

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### Contents

1 | |

2 Simple Markov population processes | 31 |

3 General Markov population processes | 107 |

4 The random walk | 199 |

5 Markov chains | 252 |

6 Markov processes in continuous time and space | 295 |

7 Modelling bivariate processes | 331 |

8 Twospecies interaction processes | 389 |

9 Spatial processes | 474 |

10 Spatialtemporal extensions | 575 |

628 | |

647 | |

### Other editions - View all

Stochastic Population Processes: Analysis, Approximations, Simulations Eric Renshaw Limited preview - 2015 |

Stochastic Population Processes: Analysis, Approximations, Simulations Eric Renshaw No preview available - 2011 |

### Common terms and phrases

algebraic algorithm analysis approach associated becomes behaviour birth birth–death process clearly coefficient colony condition consider construct corresponding cumulants cycles death rates denote determine deterministic diffusion distribution epidemic equilibrium event example exponential exponentially distributed expression extinction Figure finite follows forward equation function given gives growth hence immigration increases independent individuals infection initial integral interaction involves Kolmogorov forward equations Laplace transform linear Lotka–Volterra Markov chain mathematical matrix mean migration Moreover Note obtain occur parameter Poisson Poisson process population process power-law predators prey procedure quasi-equilibrium random variables random walk realizations recurrent Renshaw replacing result saddlepoint approximation scenarios Section shows simple random walk simulation solution spatial species step stochastic processes structure suppose theoretical trajectories ultimate extinction values variance velocity Whence whilst Wiener process yields zero