The name is absent

Taking the total derivative we get

lɪ+y^, [σ^ φ ( ^χσ—^c ) - 2σ2φ^, ( ^χσ—^c ) [^Bkr+^2x^c^r+^r²+^д^ст2∣] ^h(^χ°^c}^dc

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

and hence

√= ʃ ∞ [r [ɪ - Φ (—)] + ɪφ (—) [Bkr + 2X_cr + r² +∆σ2∣] ^dh(^xc) dX_c

dc _ J-∞ LL ' σ,- ∕J 2σv ∖ ^σv ) I ^{1 c} ' ¹ "^lJ dσχ_c ^c

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

= ʃɪ [r [ɪ - * (^χσ^-^c)] + 2⅛φ (^χσ^-^c) [Bkr+²^χcr+r²+1] ⅜¹^dχc

ɪ + - ʃɪ Φ ( ^xσ^-^c ) [r + ^x2σ^-^c [Bkr + ²^χ_cr + r² + ^21] ⅛(^χ_c )d^χ_c

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

—

ɪ— ^e√2πσχ_c

[^χ_c^-μχ_c ]²2σ2
^χc

we get

[^χc^-μχ_c ^]2

dh(Χc) ɪ - ~~2σζ

χ χc

dσχ_c √2π

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

[^χc^-μχc ]² ɪ

σ4 σ2

χ_c χ_c

and hence

_- [Xc-^μXc ]²

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

dσ_χc _- ^[^Xc^-^μXc^]2

ɪ + ɪ ʃ ∞ φ ( ' ) [r + ¾^-^c [Bkr + 2Χcr + r² + ∆σ²1] ɔ-i---e ²⁷XC dΧc

¹ σv .1 ∞ σ∙. ; L 2σJ; ^l ' ^{c 1 1 2j}J √2πσ_Xc ^c