## Abstract

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved. A class of linear, time-invariant, stochastic differential equations in real, separable, reflexive Banach spaces is formulated in such fashion that a solution of the equation is a cylindrical process. An existence and uniqueness theorem is proved. A stochastic version of the problem of heat conduction in a ring provides an example.

Original language | English |
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Pages (from-to) | 97-125 |

Number of pages | 29 |

Journal | Applied Mathematics and Optimization |

Volume | 10 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jun 1983 |

Externally published | Yes |

## ASJC Scopus subject areas

- Control and Optimization
- Applied Mathematics