## The Elements of Stochastic Processes with Applications to the Natural SciencesDevelops an introductory and relatively simple account of the theory and application of the evolutionary type of stochastic process. Professor Bailey adopts the heuristic approach of applied mathematics and develops both theoretical principles and applied techniques simultaneously. |

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### Contents

CHAPTER | 1 |

MARKOV ProCESSES in CoNTINUous TIME | 66 |

HOMOGENEOUS Birth AND DEATH PROCESSES | 84 |

SOME NONHOMOGENEOUS ProCESSES | 107 |

MultiDIMENSIONAL PROCESSES | 117 |

QUEUEING PROCESSES | 136 |

epidemic PROCESSES | 162 |

CoMPETITION AND PREDATION | 186 |

DIFFUSION PROCESSES | 194 |

APPROxiMATIONS TO STOCHAstiC PROCESSES | 207 |

SOME NONMARKovian PROCESSEs | 222 |

234 | |

AUTHOR in DEx | 243 |

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### Common terms and phrases

actual already appearing applications appropriate approximation arrival assume basic birth calculate chance Chapter coefficients consider constant continuous convenient corresponding course cumulants defined derived deterministic difficulty discrete discussion distribution easily epidemic event example expected expression extinction follows formula given gives Hence immediately important increase independent individual infectives initial condition integral interval introduced involving kind latter limiting Markov chain mathematical matrix mean method mutant namely negative obtain occur partial differential equation particular period Poisson population possible practical present probability probability distribution probability-generating function problem properties queue random variable recurrent represented respectively result Section simple situation solution solve starting stochastic Substituting successive Suppose Theorem theory transform transition trial unit usual variance whole write written yields zero