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Stochastic Hilbert integral equation in the plane. (Spanish. English summary) Zbl 0558.60046

Differential equations and applications, Proc. 7th Congr., Granada/Spain 1984, 209-214 (1985).
[For the entire collection see Zbl 0552.00006.]
The stochastic integral of biparametric Hilbert-space-valued processes with respect to biparametric Wiener operator was studied in the authors’ paper ”Stochastic integration with respect to a Hilbert-space valued Wiener operator with two parameters” XIV C.N.E.I.O.I Granada 1984, 815- 824 (1984), where they proved some of its important properties. In this work a different definition of biparametric Wiener operator is adopted, and a new stochastic integral is defined. The authors study the existence and unicity of the solution of the stochastic integral equation based on the above mentioned integral.

MSC:

60H05 Stochastic integrals
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H25 Random operators and equations (aspects of stochastic analysis)

Citations:

Zbl 0552.00006