strength prediction equations and their application

... Milan Paris Singapore Tokyo Jin Ma JiongminYong Forward-Backward Stochastic Differential Equations and Their Applications Springer Authors Jin Ma Department of Mathematics Purdue University West ... Bibliothek - CIP-Einheitsaufnahme Ma, Jin: Foreward b a c k w a r d stochastic differential equations and their applications / Jin M a ; J i o n g m i n Yong - B e r l i n , Heidelberg ; N e w York ... differential equations (PDE, for short), in the spirit of the well-known Feynman-Kac formula After this, extensive study of BSDEs was initiated, and potential for its application was found in applied and...

Ngày tải lên: 10/08/2014, 20:20

... suitable sizes, b, a, b and ~ are stochastic processes and g is a random variable We are looking for {gvt}t>0-adapted processes X(.), Y(-) and Z(-), valued in ]Rn, ]Rm and IR~, respectively, satisfying ... o n 3.2 Assume that b, a, h and ~ satisfy (2.6) Assume further that a and ~ are continuous in (t, x, y) uniformly in x, for each w E ~; and that g C C M C~(R~; R m) and is deterministic Suppose ... X, Y taking values in IRn and ]Rm, respectively Then, by Proposition 3.1, we see that for any duration T > and any dimensions n, m, ~ and d for the processes X, Y, Z and the Brownian motion W(t),...

Ngày tải lên: 10/08/2014, 20:20

... for all g C H if and only if (3.17) and (3.19) hold In this case, the adapted solution to (2.12) is unique (for any given g E H) Proof Theorems 3.2 and 3.3 tell us that (3.17) and (3.19) are necessary ... deterministic matrix-valued function and p : [0, T] • ~ + ]Rm is an {Svt)t>_0-adapted process We are going to derive the equations for P(.) and p(-) First of all, from (4.1) and the terminal condition ... hereafter in this chapter that 34 Chapter Linear Equations H = L r ( ~ ; ~ m ) and 7/ L~(0, T;~r~) (which are Hilbert spaces to which the final datum g and the process Z(.) belong, respectively)...

Ngày tải lên: 10/08/2014, 20:20

... L and T, and may change from line to line By (1.24) and (1.15), we obtain (1.25) E[Y~(T)I < EIg(X~(T)) I + ElY,(T) - g(X~(T)) I _< C(1 + Ixl) +E _< C(1 + Ixl) w Dynamic programming method and ... hold Then (i) ~ , ~ ( s , ~, y) and V ~,~(s, x, y) are continuous in (x, y) ~ " • ~ m , uniformly in s C [0, T] and 6, E >_ O; For fixed > and e > O, ~5,~ (s, x, y) and Va'~(s,x,y) are continuous ... 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 details)...

Ngày tải lên: 10/08/2014, 20:20

... 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

Ngày tải lên: 10/08/2014, 20:20

... which are C in x and C 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 T > O, (0 ... between (1.1) and (2.12) holds for adapted strong and weak solutions, respectively On the other hand, from (2.13) we see easily that the group {A, B, a, b, c} satisfies (H)m if and only if {A, ... 8~(x)h < M h Dividing h and letting h + we derive lim~-~oo 8~(x) = Further, note that ~ - a ( x , ~ [ - b ( x , ) S x + h(x)8 - 1] T h e boundedness of 8, 8~, and 8xz~ exists and is continuous expansion...

Ngày tải lên: 10/08/2014, 20:20

... (H),~ 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 b ... the Gelfand triple V r H = H' ~ +V' We denote the inner product and the induced norm of H by (-, ")0 and [-10, respectively The duality paring between V and V' is denoted by ( , ) , and the ... Gelfand triple H 1(~n) ~+ L 2(~n) ~_+H-1 (IRa) Here, H - I ( I R ~) is the dual space of H l ( ~ n ) , and the embeddings are dense and continuous We denote the duality paring between H (]Rn) and...

Ngày tải lên: 10/08/2014, 20:20

... (2.11) and working on (v,p) for the transformed equations [] Our main comparison result is the following T h e o r e m 6.2 Let (1.6), (2.2) and (H),~ hold for (6.2) and (6.3) Let (f,g) and (f,~) ... condition (2.2) and (H),~ (for some m _> 1) hold for (6.2) and (6.3) Then by Theorem 2.3, for any pairs (f, g) and (f, ~) satisfying (2.14), there exist unique adapted weak solutions (u, q) and (~, ~) ... the case that and ~ are not necessarily smooth enough, we may make approximation [] P r o p o s i t i o n 6.5 Let A, B, -5, b and -~ be independent of x Let f and be convex in x and nonnegative...

Ngày tải lên: 10/08/2014, 20:20

... [0, T]) for suitable choice of and Co Again, we let L be the common Lipschitz constant for b, a, h and g We will choose and Co so that (3.21) a(T) + 23 + c(T)L > 5, and h(t)]xI + c(t)iy] + c(t)]z] ... (5.30) and (5.32), we must have (5.29) Hence, we obtain (5.25) This shows that a strong bridge ~(t) has been constructed with K, and s being given by (5.19) and (5.28), respectively, and we may ... to see that under (3.17)-(3.18), (3.21) implies (1.8) and (3.22) implies (1.7) and (1.9)' (Note (1.8) implies (1.8)') We see that the left hand side of (3.22) can be controlled by the following:...

Ngày tải lên: 10/08/2014, 20:20

... nondecreasing and RCLL paths, such that C(0) = and C(T) < c~, a.s.-P; and E f J 17r(s)12ds < c~ Clearly, under suitable conditions, for a given strategy (Tr,C) and the initial values p > and x >_ ... complete [] Chapter Applications of FBSDEs In this chapter we collect some interesting applications of FBSDEs These applications appear in various fields of both theoretical and applied probability ... x) = 194 Chapter Applications of FBSDEs Now from the second (backward) equation in (1.2), and noting that Y0 is non-random by Blumenthal 0-1 law, we have Y0 = EYo = Eg(XT); and setting t = in...

Ngày tải lên: 10/08/2014, 20:20

... in the variables ~, x and 7r, and thus so is bo Moreover, note that for any 1-2 ~ (t, ~, ~, ~)g"(~) = l~2(t,~,x ' ~)e~2g"(~ ~) is uniformly bounded and Lipschitz in ~, x and 7r by either (H5) ... that 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 there ... SDE (4.1) We assume the following (H6) b and a are independent of 7r and are time-homogeneous; g _> and belongs boundedly to C 2+~ for some a E (0, 1); and r is uniformly bounded Define x(t) =...

Ngày tải lên: 10/08/2014, 20:20

... satisfies xh~(x) - h(x) 7_ O, and that § and are true interest rate and volatility such that they are {~'t}t_>o-adapted random fields satisfying ~(t,x) > r(t,x), and ~(t,x) > ~(t,x), V(t,x) Then, ... {Vik}, and that of 0., b, b and their partial derivatives Consequently, (2.36) ! k 1(4)}1 < C~{l~k I+ I~:~ I} +63 ' (h + At), Vk, i Use of the maximum principle and the estimates (2.33), (2.35) and ... approximation of the quasilinear PDE 245 by virtue of Theorem 2.2 and the definitions of h and At This proves (3) To show (2), let n and t be fixed, and assume that t E (t k, tk+l] Then, u (n) (t, x) = w...

Ngày tải lên: 10/08/2014, 20:20

... Buckdahn, R., and Pardoux, E., [1] Backward stochastic differential equations and integral-partial differential equations, Stochastics and Stochastics Reports, 60 (1997), 57-83 Bellman, R., and Wing, ... Nonlinear Elliptic and Parabolic Equations of the Second Order, Reidel, Dordrecht, Holland, 1987 Krylov, N N., and Rozovskii, B L., [1] Stochastic partial differential equations and diffusion processes, ... jumps and associated integral-stochastic differential equations, preprint Caffarelli, L A., and Friedman, A., [1] Partial regularity of the zero-set of semilinear and superlinear elliptic equations, ...

Ngày tải lên: 10/08/2014, 20:20

Ngày tải lên: 10/08/2014, 20:20

... CH001.tex 26/4/2007 13: 43 Page 6 Integral Equations and their Applications 1.4.2 Fredholm integral equations The most standard form of Fredholm linear integral equations is given by the form b φ(x)u(x) ... integral equations We shall outline these equations using basic definitions and properties of each type 1.4.1 Volterra integral equations The most standard form of Volterra linear integral equations ... readable and systematic manner the general theory of linear integral equations with some of its applications The applications given are to differential equations, calculus of variations, and some...

Ngày tải lên: 28/07/2016, 23:37

... article as: Zheng and Feng: Some new nonlinear integral inequalities and their applications in the qualitative analysis of differential equations Journal of Inequalities and Applications 2011 ... dsdt ∈ Dom(Y −1 ), Zheng and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20 Page 12 of 15 and β(y) u(x, y) ≤ φ −1 ... finite time Then T = ∞, and the solutions of (46) are global Zheng and Feng Journal of Inequalities and Applications 2011, 2011:20 http://www.journalofinequalitiesandapplications.com/content/2011/1/20...

Ngày tải lên: 21/06/2014, 01:20

Ngày tải lên: 13/11/2014, 09:43

... power to the faint; and to them that have no might he increaseth strength Isaiah This grace gives me fear, and this grace draws me near, And all that it asks it provides Sandra McCracken CHAPTER ... content ourselves with the M0 and M1 models for our analysis of palindromes of length four and above We are interested in deriving the mean and standard deviation of the random variable X L , total ... palindromes C k and C k+d not overlap and c denotes the segment between them (b) L ≤ d < 2L Here w denotes the common segment of palindromes C k and C k+d And w determines the left end and right end...

Ngày tải lên: 15/09/2015, 21:52

Ngày tải lên: 07/02/2013, 09:23

... √ µε Ll Cl (1.6) (1.7) In Equations (1.6) and (1.7) Ll and Cl represent the inductance and capacitance per unit length of the line, and ε and µ are the permittivity and permeability of the transmission ... these equations, d1 and d2 represent the piezoelectric charge modulus d in units and 2, respectively However, when both voltage and force are present, the following piezoelectric coupling equations ... developed using standard thin-film deposition techniques such as sputtering, and physical or chemical vapor deposition Their use in sensors and actuators is inherently limited by the quality and repeatability...

Ngày tải lên: 22/12/2013, 20:18