Mean Field Forward-Backward Stochastic Differential Equations

Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on

‫ﺍﻨﺘﻅﻤﺕ ﺍﻝﺨﻁﺔ ﻓﻲ ﻓﺼل ﺘﻤﻬﻴﺩﻱ ﻭﺜﻼﺙ ﻓﺼﻭل ﻭﺨﺎﺘﻤﺔ‪ .‬ﺘﻀﻤﻥ ﺍﻝﺘﻤﻬﻴﺩ ﺇﻁﺎﺭﺍ ﻋﺎﻤﺎ ﻋﻥ‬ ‫ﻤﻔﻬﻭﻡ ﺍﻝﻤﺸﺎﺭﻜﺔ ﺍﻝﺴﻴﺎﺴﻴﺔ ﻤﻥ ﺨﻼل ﺘﻌﺭﻴﻔﻬﺎ‪ ،‬ﻤﺴﺘﻭﻴﺎﺘﻬﺎ‪

Key W ords: Adapted solution, antiipating stohasti alulus, bakward doubly SDEs,.. stohasti partial dierential equation, stohasti

[9] Gozzi F., Marinelli C., Stochastic optimal control of delay equations arising in advertising models, Da Prato (ed.) et al., Stochastic partial differential equations

Eventually, we connect the forward and backward stochastic differential equations with normal constraints in law with partial differential equations stated on the Wasserstein space

Finally, assuming that for each i = 1, · · · , n, the ith component g i of the generator g is Lipschitz continuous in the state variable y, depends only on the ith row z i of the

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Flow cytometric analyses of CD8 þ T cells for NKG2D expression and (b) prognosis value shown by Kaplan- Meier overall survival (OS) curves segregating the cohort of metastatic