Given fixed ((t,x in[0, T]timesmathbb{R}), we note that (Phi (t,x =Y^{t,x}_{t}) is an adapted solution of the anticipated BSDE (14).
A process ((x cdot),y(cdot),z(cdot),k(cdot,cdot),p cdot),q(cdot),r(cdot ),theta(cdot,cdot))inmathcal{L}[0,T]) is called an adapted solution of FBSDE (3) if it satisfies (3).
For any (alpha in mathbb{R}), a stochastic process (X_{alpha }(cdot) in C_{mathbb{F}}([0,T] L^{2}(Omega ;mathbb{R}^{m}))) is called an adapted solution to SVIE (1.1) on ([0,T]) if (1.1) holds in the usual Itô's sense for all (tin[0,T]).
A triple of processes ((X,Y,Z): Omegatimes [0,T] rightarrowmathbb{R}^{n}timesmathbb{R}^{m}times mathbb{R}^{mtimes d}) is called an adapted solution of the FBSDE (1) if ((X,Y,Z inmathcal {M}^{2}(0,T;mathbb{R}^{mtimessmathbb{R}^{m}times mathbb{R}^{mtimes d})) and it satisfies FBSDE (1) (mathbb{P} -almost surely.
Then it follows from Theorem 3.3 that the GRE (2.6) admits a regular solution (P. To determine u ∗, let (X ∗,Y ∗,Z ∗ be the adapted solution of (3.1).
If there exists a unique adapted solution, then (3) is said to be uniquely solvable.
For any (alpha in mathbb{R}), stochastic processes pair ((Y_{alpha }(cdot),Z_{alpha }(cdot,cdot))inmathcal{H}^{2}[S,T]) is called an adapted M-solution to BSVIE (1.2) on ([S,T]) if (1.2) holds in the usual Itô's sense for almost all (tin [S,T]) and, in addition, the following holds: Y_{alpha }(t)=mathbb{E}bigl(Y_{alpha }(t)|mathcal{F}_{S}bigr)+ int_{S}^{t} Z_{alpha } t,s),dW s), quad mbox{a.e.e
"We spent a lot of time thinking about our experience [at Canesta] and said let's focus on what would be an ideal solution: the machine should adapt to you and should react to the way you are trying to communicate with it".
CBR is an original paradigm to adapt solutions of past problems in order to solve new similar problems.
This makes SISTPV systems to be a versatile solution that can be adapted for operation in a broad range of locations with different climate conditions, even being used off-grid and in space applications.
