Differential Equations and Their Applications Part 12 pot
Differential Equations and Their Applications Part 12 pot
... both al and f12 are adapted processes and are uniformly bounded in (t, w). Similarly, by conditions (H1) (H3) and (H5'), we see that the process O(.,P(.)) is uniformly bounded and that ... x* ~=X(O) is the 212 Chapter 8. Applications of FBSDEs Proof. First consider the function 0"~ O -g. It is obvious that 0t = 0t, Op = Op - gp and Opp = Opp - gpp; and 0"...
Ngày tải lên: 10/08/2014, 20:20
Differential Equations and Their Applications Part 13 pot
... (A1) and (A2), one can show that w i as io + co, uniformly in i and k. In particular, if we fix the mesh size h > 0, and let R = ioh, then the quantities (2.8) maxlu(tk,x~) wk[ and max ... {Vik}, and that of 0., b, b and their partial derivatives. Consequently, ! k 1 k 1 ' (h + At), Vk, i. (2.36) 1(4)}1 < C~{l~ I+ I~:~ I} +63 Use of the maximum principle...
Ngày tải lên: 10/08/2014, 20:20
Differential Equations and Their Applications Part 4 ppsx
... (i) ~,~(s, ~, y) and V ~,~(s, x, y) are continuous in (x, y) 9 ~" • ~m, uniformly in s C [0, T] and 6, E >_ O; For fixed 6 > 0 and e > O, ~5,~ (s, x, y) and Va'~(s,x,y) ... similar to that of Proposition 3.1 and the proof of (ii) and (iii) are by now standard, which we omit here for simplicity of presentation (see Yong-Zhou [1] and Fleming-Soner [1], for...
Ngày tải lên: 10/08/2014, 20:20
Differential Equations and Their Applications Part 5 pptx
... -/3) EIZ(s) - Z(s)12ds ~t T (1.15) < C E{I:Y(s) - V(s)l 2 + [Y(s) - y(s)lLZ(s) - Z(s)l}ds __ c~ El~(s) - Y(s)12as + s 12( s) - Z(s)12as, where e > 0 is arbitrary and C~ depends on ... of the coefficients of the system (2.1) (i.e., b, h, a, and 3(z) - z) and their derivatives. Therefore using assumptions (H1) and (H4), and noting that supt IZ(k)(t)l <_ sup Is...
Ngày tải lên: 10/08/2014, 20:20
Differential Equations and Their Applications Part 6 ppt
... in x and C 1 in t with H51der continuous v,~s and vt of exponent a and a12, respectively. Moreover, we have (3.54) IwR(t,x)l < M, (t,x) e [0,~) • BR, and for any Xo C ~" and ... with random coefficients, i.e., b, a, h and g are possibly depending on w E ~ explicitly, then it will lead to the study of general degenerate nonlinear backward partial differential...
Ngày tải lên: 10/08/2014, 20:20
Differential Equations and Their Applications Part 7 docx
... if and only if {A,B,~d,b,c} satisfies (H),~, where ~ and b are given by (1.4). Thus, we have the exact statements as Theorems 2.1, 2.2 and 2.3 for BSPDE (1.5) with a and b replaced by ~ and ... and V' is denoted by (.,.)0, and the norms of V and V' are denoted by 1]" I[ and I[" []*, respectively. We know that the following holds: (3 .12) (u,v)0=(u,v...
Ngày tải lên: 10/08/2014, 20:20
Differential Equations and Their Applications Part 8 pps
... (2.11) and working on (v,p) for the transformed equations. [] Our main comparison result is the following. Theorem 6.2. Let (1.6), (2.2) and (H),~ hold for (6.2) and (6.3). Let (f,g) and (f,~) ... /o/ < ce {1 ~12 + El~ol 2 + E {INo(t)l 2 + I~o(t)l 2 + I'~o(t )12} dt} (2.18) +2-~E foT{If'(i)]2+l~(t)]2}dt // cUE 12( T)I 2~ + I~ol ~ + {12( t)l 2 + I'~o(...
Ngày tải lên: 10/08/2014, 20:20