The name is absent



Taking the total derivative we get

lɪ+y,   [σ^ φ ( χσ—c ) - 2σ2φ, ( χσc ) [Bkr+2xcr+r2+дст2] h(χ°^c}dc

{£ [r [ɪ - *    ■ i)] + ⅛φ    ■  c) [Bkr + . Xcr + 2 + ∆σ2∣]    "«.} d = 0

and hence

√=       ʃ ∞ [r [ɪ - Φ (—)] + ɪφ (—) [Bkr + 2Xcr + r2 +∆σ2] dh(xc) dXc

dc     _    J-∞ LL        ' σ,- ∕J    2σv ∖ σv ) I 1 c ' 1 "lJ χc c

χc  -  ɪ + - ʃɪ [rφ (χσ∏ - ⅛φ' (χσ-) [Bkr+2χr+r2+^2] ⅛(χc)dχc

=  ʃɪ [r [ɪ - * (χσ-c)] + 2⅛φ (χσ-c) [Bkr+2χcr+r2+1] 1 c

ɪ + - ʃɪ Φ ( xσ-c ) [r + x2σ-c [Bkr + 2χcr + r2 + ^21] ⅛(χc )dχc

where the second line uses the fact that φ'(x) =


ɪ— e
√2πσχc


[χc-μχc ]2
2
σ2
χc


we get


[χc-μχc ]2

dh(Χc)      ɪ - ~~2σζ

χ      χc

χc     √2π


(x). Assuming a normal density h(Xc) =


[χc-μχc ]2      ɪ

σ4       σ2

χc        χc


and hence


- [Xc-μXc ]2

d-c    σXc ʃɪ [r - * (χσ-c)] + 2⅛φ (χσ-c) [Bkr + 2χcr+ r2 + ^2]][ɪ-  χ -X x     ^∏σχ-e   2σχc  c

χc                                                                                                   - [Xc-μXc]2

ɪ + ɪ ʃ φ ( '   ) [r + ¾-c [Bkr + cr + r2 + ∆σ21] ɔ-i---e   27XC  c

1 σv .1 ∞        σ∙. ; L        2σJ; l ' c 1       1      2jJ √2πσXc                          c

33



More intriguing information

1. The name is absent
2. Chebyshev polynomial approximation to approximate partial differential equations
3. Name Strategy: Its Existence and Implications
4. Commuting in multinodal urban systems: An empirical comparison of three alternative models
5. Towards a Strategy for Improving Agricultural Inputs Markets in Africa
6. The Effects of Reforming the Chinese Dual-Track Price System
7. The name is absent
8. Menarchial Age of Secondary School Girls in Urban and Rural Areas of Rivers State, Nigeria
9. The Value of Cultural Heritage Sites in Armenia: Evidence From a Travel Cost Method Study
10. Motivations, Values and Emotions: Three Sides of the same Coin