Partial Differential Equations as Equations in Infinite Dimensions

2011 ◽  
pp. 3-16
Author(s):  
Leszek Gawarecki ◽  
Vidyadhar Mandrekar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Infinite Dimensions ◽  
Partial Differential

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

scholarly journals Optimal control for stochastic partial differential equations and viscosity solutions of Bellman equations

1991 ◽  
Vol 123 ◽  
pp. 13-37 ◽  
Author(s):  
Makiko Nisio
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Viscosity Solutions ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Infinite Dimensions ◽  
Partial Differential ◽  
Bellman Equations

Recently M. G. Crandall and P. L. Lions developed the viscosity theory on nonlinear equations in infinite dimensions and optimal control in Hilbert spaces, in two series of papers, [1], [4].

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