Stochastic Integration in Abstract Spaces | Zendy

James K. Brooks | Zendy; J. T. Kozinski | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Stochastic Integration in Abstract Spaces

Author(s) -

James K. Brooks,

J. T. Kozinski

Publication year - 2010

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2010/217372

Subject(s) - mathematics , integrable system , pure mathematics , dual polyhedron , lp space , square integrable function , hilbert space , reflexive space , martingale (probability theory) , stochastic integral , banach space , mathematical analysis , discrete mathematics , interpolation space , biochemistry , chemistry , functional analysis , stochastic differential equation , gene

We establish the existence of a stochastic integral in a nuclear space settingas follows. Let , , and be nuclear spaces which satisfy the followingconditions: the spaces are reflexive, complete, bornological spaces such that theirstrong duals also satisfy these conditions. Assume that there is a continuousbilinear mapping of × into . If is an integrable, -valued predictableprocess and is an -valued square integrable martingale, then there exists a-valued process (∫) called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research