Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

ON STOCHASTIC EVOLUTION EQUATIONS WITH STATE-DEPENDENT DIFFUSION TERMS

  • Published : 1997.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

The integral solution for a deterministic evolution equation was introduced by Benilan. Similarly, in this paper, we define the integral solution for a stochastic evolution equation with a state-dependent diffusion term and prove that there exists a unique integral solution of the stochastic evolution euation under some conditions for the coefficients. Moreover we prove that this solution is a unique strong solution.

Keywords

References

  1. Nonlinear Semigroups and Differential Equations in Banach spaces V. Barbu
  2. Seminaire Deny sur les semingroupes nonlineaires Solutions faibles d'equations d'evolution dans un espace reflexif P. Benilan
  3. Lecture Nores in Control and Information Sciences v.8 Infinite Dimensional Linear Systems Theory R. F. Curtain;A. J. Pritchard
  4. J. Differential Equations v.68 $^*$-solution of evolution equations in Hilbert space D. A. Dawson
  5. Stochastic Analysis and Applications v.14 On nonlinear stochastic evolution equations J. H. Kim
  6. Carleton Mathematical lecture Notes Stochastic Evolution Equations and White Noise Analysis Y. Miyahara
  7. Stochastics v.3 Stochastic Partial Differential Equations and Filtering of Diffusion Processes E. Pardoux.