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Stochastic Differential Equations

  • Gopinath Kallianpur
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 13)

Abstract

Denote by C d = C([0,T],R d ), d ≥ 1 the space of continuous functions on [0,T] taking values in R d . Let S be a complete, separable metric space and D = D([0,T],S), the space of right-continuous functions from [0,T] to S having left-hand limits Let ℬ t (C d ) be the minimal σ-field with respect to which the coordinate functions \(f\left( s \right)\left( {0 \leqslant s \leqslant t,f \in C_d } \right) \) are measurable. The a-field ℬ(D) is similarly defined. We write ℬ(C d ) = ℬ T (C d ) and ℬ(D) = ℬ T (D).

Keywords

Weak Solution Markov Process Stochastic Differential Equation Strong Solution Wiener Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gopinath Kallianpur
    • 1
  1. 1.Department of StatisticsUniversity of North CarolinaChapel HillUSA

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