## An Introduction to Infinite-Dimensional AnalysisIn this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic functional analysis and measure theory but not necessarily probability theory – to analysis in a separable Hilbert space of infinite dimension. Starting from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate some basic stochastic dynamical systems (including dissipative nonlinearities) and Markov semi-groups, paying special attention to their long-time behavior: ergodicity, invariant measure. Here fundamental results like the theorems of Prokhorov, Von Neumann, Krylov-Bogoliubov and Khas'minski are proved. The last chapter is devoted to gradient systems and their asymptotic behavior. |

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### Contents

IX | 14 |

X | 16 |

XI | 17 |

XII | 20 |

XIII | 24 |

XVI | 25 |

XVII | 29 |

XVIII | 31 |

XIX | 33 |

XX | 38 |

XXI | 41 |

XXII | 44 |

XXIII | 46 |

XXIV | 47 |

XXV | 49 |

XXVII | 55 |

XXVIII | 56 |

XXIX | 58 |

XXX | 65 |

XXXI | 67 |

XXXIII | 71 |

XXXIV | 74 |

XXXV | 75 |

XXXVI | 77 |

XXXVII | 79 |

XXXVIII | 82 |

XL | 84 |

XLI | 88 |

XLII | 92 |

XLIV | 94 |

XLV | 97 |

XLVII | 100 |

XLVIII | 104 |

XLIX | 108 |

LX | 130 |

LXI | 133 |

LXII | 135 |

LXIV | 137 |

LXV | 139 |

LXVI | 140 |

LXVII | 141 |

LXVIII | 143 |

LXIX | 144 |

LXX | 147 |

LXXI | 148 |

LXXII | 150 |

LXXIII | 154 |

LXXIV | 158 |

LXXV | 160 |

LXXVI | 163 |

LXXVII | 164 |

LXXVIII | 167 |

LXXIX | 169 |

LXXX | 171 |

LXXXI | 173 |

LXXXII | 175 |

LXXXIV | 178 |

LXXXV | 181 |

LXXXVI | 186 |

LXXXVII | 187 |

LXXXVIII | 189 |

LXXXIX | 191 |

XC | 194 |

XCI | 198 |

XCII | 202 |

XCIII | 203 |

XCIV | 206 |

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### References to this book

Control Theory of Partial Differential Equations Guenter Leugering,Oleg Imanuvilov,Bing-Yu Zhang,Roberto Triggiani No preview available - 2005 |