Stochastic Differential Equations

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


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).


Weak Solution Markov Process Stochastic Differential Equation Strong Solution Wiener Process 
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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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