Solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations. Parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control.
Fuhrman, M., Tessitore, G. (2002). Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control. ANNALS OF PROBABILITY, 30(3), 1397-1465 [10.1214/aop/1029867132].
Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control
TESSITORE, GIANMARIO
2002
Abstract
Solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations. Parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control.
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