ࡱ>   ``bjbj ye: : : (b  RRR8R,"U )2U^^:^`_&z ((((((($*h1-( d|&dd( ^`_JeQ)hhhd ^p `_(hd(hhd 0 (`_U P/:R<44"(|g)0)h...h((b. 46jhDB"444((d444)dddd /z=D z=  8653>@>4A:89 3>AC40@AB25==K9 C=825@A8B5B 8<. .. >10G52A:>3>  TITLE \* MERGEFORMAT 5:F8>==K5 <0B5@80;K. ;020 1. 2545=85 2 <5B>4K >=B5-0@;> 86=89 >23>@>4 2005 ;020 1. 2545=85 2 <5B>4K >=B5-0@;> !>45@60=85  TOC \o "2-4" \h \z \t "Heading 1,1"  HYPERLINK \l "_Toc122509360" 2545=85  PAGEREF _Toc122509360 \h 3  HYPERLINK \l "_Toc122509361" !B0B8AB8G5A:>5 <>45;8@>20=85 :0: =0CG=>5 =0?@02;5=85  PAGEREF _Toc122509361 \h 5  HYPERLINK \l "_Toc122509362" >=OB85 AB0B8AB8G5A:>3> <>45;8@>20=8O  PAGEREF _Toc122509362 \h 5  HYPERLINK \l "_Toc122509363" !E5<0 ?@>2545=8O 2KG8A;5=89 2 AB0B8AB8G5A:>< <>45;8@>20=88  PAGEREF _Toc122509363 \h 5  HYPERLINK \l "_Toc122509364" 1;0AB8 ?@8<5=5=8O AB0B8AB8G5A:>3> <>45;8@>20=8O  PAGEREF _Toc122509364 \h 6  HYPERLINK \l "_Toc122509365" 5B>4 AB0B8AB8G5A:8E 8A?KB0=89 (<5B>4K >=B5-0@;>). AB>@8O <5B>40  PAGEREF _Toc122509365 \h 7  HYPERLINK \l "_Toc122509366" 5B>4K >=B5-0@;>. =0;87 >1I59 AE5<K, 4>AB>8=AB20 8 =54>AB0B:8  PAGEREF _Toc122509366 \h 8  HYPERLINK \l "_Toc122509367" @8<5@K ?@8<5=5=8O <5B>4>2 >=B5-0@;>  PAGEREF _Toc122509367 \h 9  HYPERLINK \l "_Toc122509368" 040G0 2KG8A;5=8O ?;>I048 D83C@K =0 ?;>A:>AB8  PAGEREF _Toc122509368 \h 10  HYPERLINK \l "_Toc122509369" 040G0 >F5=820=8O G8A;0 (  PAGEREF _Toc122509369 \h 11  HYPERLINK \l "_Toc122509370" 3;0 NDD>=0  PAGEREF _Toc122509370 \h 11  HYPERLINK \l "_Toc122509371" 5B>4 Hit-Or-Miss  PAGEREF _Toc122509371 \h 15  HYPERLINK \l "_Toc122509372" 5B>4 K1>@>G=>3> A@54=53>  PAGEREF _Toc122509372 \h 16  HYPERLINK \l "_Toc122509373" !;CG09=>ABL 8 8<8B0F8O A;CG09=>AB8  PAGEREF _Toc122509373 \h 18  HYPERLINK \l "_Toc122509374" !;CG09=>ABL 8 =5?@54A:07C5<>ABL  PAGEREF _Toc122509374 \h 18  HYPERLINK \l "_Toc122509375" !;CG09=K5 G8A;0 8 35=5@0B>@K A;CG09=KE G8A5;  PAGEREF _Toc122509375 \h 19  HYPERLINK \l "_Toc122509376" 5=5@0B>@K ?A524>A;CG09=KE G8A5; (PRNG)  PAGEREF _Toc122509376 \h 19  HYPERLINK \l "_Toc122509377" 0:;NG5=85  PAGEREF _Toc122509377 \h 22  HYPERLINK \l "_Toc122509378" 8B5@0BC@0  PAGEREF _Toc122509378 \h 23 2545=85 A;8 ;N48 =5 ?>;030NB, GB> <0B5<0B8:0 ?@>AB0, B> B>;L:> ?>B><C, GB> >=8 =5 ?>=8<0NB, :0: =0 A0<>< 45;5 A;>6=0 687=L. 6>= D>= 59<0= >1@K9 45=L, C20605<K9 G8B0B5;L! @5645 2A53>, E>B5;>AL 1K :@0B:> >E0@0:B5@87>20BL :C@A, :>B>@K9 K =0G8=05B5 87CG0BL. 0G=5< A @0AH8D@>2:8 =0720=8O !B0B8AB8G5A:>5 <>45;8@>20=85 8 ?0@0;;5;L=K5 2KG8A;5=8O. !B0B8AB8G5A:>5 <>45;8@>20=85  G8A;5==K9 <5B>4 @5H5=8O <0B5<0B8G5A:8E 7040G, ?@8 :>B>@>< 8A:><K5 25;8G8=K ?@54AB02;ONB 25@>OB=>AB=K<8 E0@0:B5@8AB8:0<8 :0:>3>-;81> A;CG09=>3> O2;5=8O, MB> O2;5=85 <>45;8@C5BAO, ?>A;5 G53> =C6=K5 E0@0:B5@8AB8:8 ?@81;86Q==> >?@545;ONB ?CBQ< AB0B8AB8G5A:>9 >1@01>B:8 =01;N45=89 <>45;8 [ REF _Ref119825896 \r \h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B0:, 70 45;>! !B0B8AB8G5A:>5 <>45;8@>20=85 :0: =0CG=>5 =0?@02;5=85 @5645 2A53>, ?>?@>1C5< ?>B>G=55 ?>=OBL, GB> A:@K205BAO 70 B08=AB25==K< =0720=85< !B0B8AB8G5A:>5 <>45;8@>20=85. 1@0B8<AO : >;LH>9 !>25BA:>9 -=F8:;>?5488 (!-). >=OB85 AB0B8AB8G5A:>3> <>45;8@>20=8O !B0B8AB8G5A:>5 <>45;8@>20=85  G8A;5==K9 <5B>4 @5H5=8O <0B5<0B8G5A:8E 7040G, ?@8 :>B>@>< 8A:><K5 25;8G8=K ?@54AB02;ONB 25@>OB=>AB=K<8 E0@0:B5@8AB8:0<8 :0:>3>-;81> A;CG09=>3> O2;5=8O, MB> O2;5=85 <>45;8@C5BAO, ?>A;5 G53> =C6=K5 E0@0:B5@8AB8:8 ?@81;86Q==> >?@545;ONB ?CBQ< AB0B8AB8G5A:>9 >1@01>B:8 =01;N45=89 <>45;8. 0?@8<5@, B@51C5BAO @0AAG8B0BL ?>B>:8 B5?;0 2 =03@5205<>9 B>=:>9 <5B0;;8G5A:>9 ?;0AB8=5, =0 :@0OE :>B>@>9 ?>445@68205BAO =C;520O B5<?5@0BC@0. 0A?@545;5=85 B5?;0 >?8AK205BAO B5< 65 C@02=5=85<, GB> 8 @0A?;K20=85 ?OB=0 :@0A:8 2 A;>5 684:>AB8. >MB><C <>45;8@CNB ?;>A:>5 1@>C=>2A:>5 42865=85 G0AB8F :@0A:8 ?> ?;0AB8=5, A;54O 70 8E ?>;>65=8O<8 2 <><5=BK tk, k = 0, 1, 2,... @81;86Q==> ?@8=8<0NB, GB> 70 <0;K9 8=B5@20; t G0AB8F0 ?5@5<5I05BAO =0 H03 h @02=>25@>OB=> 2> 2A5E =0?@02;5=8OE. 064K9 @07 =0?@02;5=85 2K18@05BAO A;CG09=K< >1@07><, =57028A8<> >B 2A53> ?@54K4CI53>. !>>B=>H5=85 <564C t 8 h >?@545;O5BAO :>MDD8F85=B>< B5?;>?@>2>4=>AB8. 2865=85 =0G8=05BAO 2 8AB>G=8:5 B5?;0 8 :>=G05BAO ?@8 ?5@2>< 4>AB865=88 :@0O (=01;N405BAO =0;8?0=85 :@0A:8 =0 :@09). >B>: Q(C) B5?;0 G5@57 CG0AB>: ! 3@0=8FK 87<5@O5BAO :>;8G5AB2>< =0;8?H59 :@0A:8. @8 >1I5< :>;8G5AB25 N G0AB8F A>3;0A=> 70:>=C 1>;LH8E G8A5; B0:0O >F5=:0 40QB >H81:C ?>@O4:0  EMBED Equation.DSMT4 . [ REF _Ref119825896 \r \h 14] !E5<0 ?@>2545=8O 2KG8A;5=89 2 AB0B8AB8G5A:>< <>45;8@>20=88 !B0B8AB8G5A:>5 <>45;8@>20=85 ?@54?>;0305B A;54CNICN AE5<C 2KG8A;5=8O (>F5=820=8O) 8A:><>9 25;8G8=K. "0:, 8A:><CN 25;8G8=C ?@54AB02;ONB <0B5<0B8G5A:8< >6840=85< G8A;>2>9 DC=:F88 f >B A;CG09=>3> 8AE>40 w =5:>B>@>3> O2;5=8O:  EMBED Equation.DSMT4 , (1.1) B. 5. 8=B53@0;>< ?> 25@>OB=>AB=>9 <5@5  [ REF _Ref119825896 \r \h 14]. "0:8< >1@07><, 4;O B>3>, GB>1K >F5=8BL =5:>B>@>5 7=0G5=85, =5>1E>48<> ?>4>1@0BL A;CG09=CN 25;8G8=C B0:, GB>1K 55 <0B5<0B8G5A:>5 >6840=85 @02=O;>AL 8A:><><C 7=0G5=8N. >A;5 MB>3> <>6=> ?@>=01;N40BL A;CG09=CN 25;8G8=C 8 >F5=8BL ?> 2K1>@:5 55 <0B5<0B8G5A:>5 >6840=85. >;CG5==K9 @57C;LB0B <>6=> AG8B0BL >F5=:>9 8A:><>3> 7=0G5=8O. 0AA<>B@8< >F5=:C <0B5<0B8G5A:>3> >6840=8O A;CG09=>9 25;8G8=K  EMBED Equation.DSMT4  (1.2) 345  EMBED Equation.DSMT4   8AE>4K, A>AB>O2H85AO 2 @57C;LB0B5 =01;N45=89. F5=:C (1.2) <>6=> @0AA<0B@820BL :0: :204@0BC@=CN D>@<C;C 4;O C:070==>3> 8=B53@0;0 A> A;CG09=K<8 C7;0<8  EMBED Equation.DSMT4  8 A;CG09=>9 ?>3@5H=>ABLN  EMBED Equation.DSMT4 . "0:8< >1@07><, @0AA<0B@8205<0O AE5<0 A>AB>8B 2 ?@>2545=88 A5@88 M:A?5@8<5=B>2. 064K9 i-K9 M:A?5@8<5=B ?@54AB02;O5B A>1>9 ?>;CG5=85 A;CG09=>3> 8AE>40  EMBED Equation.DSMT4  8 2KG8A;5=85 DC=:F88 f( EMBED Equation.DSMT4 ). >A;5 MB>3> ?@>872>4OBAO 2KG8A;5=8O ?> D>@<C;5 (1.2) 8 ?>;CG5==K9 @57C;LB0B AG8B05BAO >F5=:>9 8A:><>9 25;8G8=K. !;CG09=K9 2K1>@ =0 :064>< MB0?5 ?@>2>48BAO A ?><>ILN A;CG09=KE G8A5;, :>B>@K5 =5>1E>48<> 35=5@8@>20BL B5< 8;8 8=K< >1@07><. 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CABL B5?5@L <K ?@>872>;L=K< >1@07>< 1@>A05< =0 ?;>A:>ABL 83;C 4;8=K  EMBED Equation.DSMT4 . >?@>A: :0:>20 25@>OB=>ABL B>3>, GB> 83;0 ?5@5A5G5B >4=C 87 ?@O<KE? ;O @5H5=8O 7040G8 ?>A<>B@8< =0 @8A. 1.2.  SHAPE \* MERGEFORMAT  8A. 1.2 3;0 NDD>=0. >;>65=85 83;K =B5@5ACNI55 =0A ?>;>65=85 83;K =0 ?;>A:>AB8 (y-:>>@48=0B0 =58=B5@5A=0) >?8AK205BAO 42C<O ?0@0<5B@0<8 (42C<O =57028A8<K<8 A;CG09=K<8 25;8G8=0<8): :>>@48=0B>9 >4=>3> 87 :>=F>2 h 8 C3;>< ?>2>@>B0 >B=>A8B5;L=> 3>@87>=B0;L=>9 >A8  EMBED Equation.DSMT4 . G5284=>,  EMBED Equation.DSMT4 . =>65AB2> 2>7<>6=KE ?>;>65=89 83;K F5;8:>< >?@545;O5BAO A;CG09=K< 2K1>@>< B>G:8 87 >1;0AB8 F(h,  EMBED Equation.DSMT4 ) =  EMBED Equation.DSMT4 . 0AA<>B@8< A>1KB85 A  83;0 ?5@5A5:05B ?> ?@O<CN x = d.  EMBED Equation.DSMT4  (1.4) 0@8AC5< 2 ?;>A:>AB8  EMBED Equation.DSMT4  >1;0ABL, A>>B25BAB2CNICN A>1KB8N A.  SHAPE \* MERGEFORMAT  8A. 1.3 3;0 NDD>=0. #A;>285 ?5@5A5G5=8O 0945< ?;>I04L S+ MB>9 >1;0AB8. 1>7=0G8< G5@57 S ?;>I04L 2A53> ?@O<>C3>;L=8:0, >B25G0NI53> ?@>AB@0=AB2C M;5<5=B0@=KE 8AE>4>2, 0 S-  ?;>I04L ?>4 :@82>9  EMBED Equation.DSMT4  > >?@545;5=8N S = S+ + S-. 0945<  EMBED Equation.DSMT4 . "5?5@L 25@>OB=>ABL A>1KB8O A <>65B 1KBL 2KG8A;5=0 :0:  EMBED Equation.DSMT4  B0:, 25@>OB=>ABL B>3>, GB> 83;0 ?5@5A5G5B ?@O<CN B5>@5B8G5A:8 5ABL  EMBED Equation.DSMT4  (1.5) C45< ?@>2>48BL M:A?5@8<5=B ?> 1@>A0=8N 83;K N @07, @538AB@8@CO 2 :064>< M:A?5@8<5=B5 D0:B =0ABC?;5=8O/=5 =0ABC?;5=8O A>1KB8O A. 0AA<>B@8< A;CG09=CN 25;8G8=C  EMBED Equation.DSMT4 . 2545<  EMBED Equation.DSMT4 G0AB>B0 =0ABC?;5=8O A>1KB8O A. ">340  EMBED Equation.DSMT4 , ?@8G5< 40==K5 8AE>4K =5 @02=>25@>OB=K. 725AB=>, GB> A;CG09=0O 25;8G8=0  EMBED Equation.DSMT4  ?>4G8=O5BAO 18=><80;L=><C @0A?@545;5=8N. ?@545;8< ?0@0<5B@K @0A?@545;5=8O.  EMBED Equation.DSMT4  C45< @0AA<0B@820BL  EMBED Equation.DSMT4   G0AB>BC =0ABC?;5=8O A>1KB8O A  2 :0G5AB25 >F5=:8 25;8G8=K p  25@>OB=>AB8 B>3>, GB> 83;0 ?5@5A5:05B >4=C 87 ?@O<KE. =0O B5>@5B8G5A:CN 25@>OB=>ABL MB>3> A>1KB8O  EMBED Equation.DSMT4 , <K <>65< >F5=8BL MBC 25@>OB=>ABL ?> 4>AB0B>G=> 1>;LH>9 2K1>@:5 ( EMBED Equation.DSMT4 ) 8 @0AA<>B@5BL A;54CNI55 @025=AB2>:  EMBED Equation.DSMT4  (1.6) ">340  EMBED Equation.DSMT4  (1.7) >?@>1C5< ?>=OBL, =0A:>;L:> E>@>H0 >F5=:0 (1.7). ;O MB>3> 4>:065< @O4 CB25@645=89. #B25@645=85  EMBED Equation.DSMT4 , B.5.  EMBED Equation.DSMT4   =5A<5I5==0O >F5=:0 7=0G5=8O p. >:070B5;LAB2>: #G8BK20O, GB> 25;8G8=0 SN 5ABL @57C;LB0B 2K?>;=5=8O N =57028A8<KE 8A?KB0=89 (18=><80;L=>5 @0A?@545;5=85), 8<55<:  EMBED Equation.DSMT4 , G.B.4. 5A;>6=> ?>:070BL, GB>  EMBED Equation.DSMT4   MDD5:B82=0O >F5=:0 p (>F5=:0 A =08<5=LH59 48A?5@A859), 0 B0:65 A>AB>OB5;L=0O >F5=:0 p (AE>48BAO ?> 25@>OB=>AB8 : p). B0:, 3>2>@O =5D>@<0;L=K< O7K:><, =0945==0O =0<8 >F5=:0 O2;O5BAO 4>2>;L=> =5?;>E>9 ?@8 4>AB0B>G=> 1>;LH>< :>;8G5AB25 8A?KB0=89 N. 0AA<>B@8< 2>?@>A, A2O70==K9 A 5I5 >4=8< :@09=5 65;0B5;L=K< A2>9AB2>< >F5=:8  C<5=LH5=85< 55 48A?5@A88. ;O B>3> GB>1K ?>4>1@0BL ?0@0<5B@K M:A?5@8<5=B0 B0:, GB>1K 48A?5@A8O 1K;0 <8=8<0;L=>9, =5>1E>48<> @5H8BL 7040GC <8=8<870F88  EMBED Equation.DSMT4  (1.8) 5H82 7040GC, ?>;CG05<, GB> <8=8<C< 4>AB8305BAO ?@8 l = d. ">340  EMBED Equation.DSMT4 . ;O 8A:;NG5=8O 2K@>645==>3> A;CG0O SN = 0 >?@545;8< =0HC >F5=:C G8A;0 ( A;54CNI8< >1@07><:  EMBED Equation.DSMT4  (1.9) >6=> ?>:070BL, GB> >F5=:0 (1.9) AE>48BAO ?> 25@>OB=>AB8 : (. 5B>4 Hit-Or-Miss I5 >48= <5B>4 >F5=820=8O G8A;0 ( =07K205BAO Hit-Or-Miss (?>?0;  =5 ?>?0;). 5B>4 A>AB>8B 2 A;54CNI5<: @0AA<>B@8< 548=8G=K9 :204@0B =0 :>>@48=0B=>9 ?;>A:>AB8 8 G5B25@BL >:@C6=>AB8 548=8G=>3> @048CA0 A F5=B@>< 2 =0G0;5 :>>@48=0B (@8A. 1.4).  SHAPE \* MERGEFORMAT  8A. 1.4 5B>4 Hit-Or-Miss CABL 548=8G=K9 M:A?5@8<5=B A>AB>8B 2 B><, GB> 2 548=8G=>< :204@0B5 A;CG09=> 2K18@05BAO ;N10O B>G:0. 0AA<>B@8< A>1KB85 A, A>AB>OI55 2 B><, GB> B>G:0 ?>?0;0 2 @0AA<0B@8205<K9 A5:B>@ >:@C6=>AB8. ;>I04L :204@0B0 Smax = 1, ?;>I04L 2K45;5==>9 >1;0AB8  EMBED Equation.DSMT4 . 0AA<>B@8< A;CG09=CN 25;8G8=C  EMBED Equation.DSMT4 . 2545<  EMBED Equation.DSMT4 G0AB>B0 =0ABC?;5=8O A>1KB8O A. ">340  EMBED Equation.DSMT4 , A;CG09=0O 25;8G8=0  EMBED Equation.DSMT4  ?>4G8=O5BAO 18=><80;L=><C @0A?@545;5=8N. ?@545;8< ?0@0<5B@K @0A?@545;5=8O.  EMBED Equation.DSMT4  C45< @0AA<0B@820BL  EMBED Equation.DSMT4   G0AB>BC =0ABC?;5=8O A>1KB8O A  2 :0G5AB25 >F5=:8 25;8G8=K p  25@>OB=>AB8 B>3>, GB> B>G:0 ?>?0;0 2 C:070==K9 A5:B>@ >:@C6=>AB8. =0O B5>@5B8G5A:CN 25@>OB=>ABL MB>3> A>1KB8O  EMBED Equation.DSMT4 , <K <>65< >F5=8BL MBC 25@>OB=>ABL ?> 4>AB0B>G=> 1>;LH>9 2K1>@:5 ( EMBED Equation.DSMT4 ) 8 @0AA<>B@5BL A;54CNI55 @025=AB2>:  EMBED Equation.DSMT4  (1.10) ">340 <>6=> @0AA<>B@5BL  EMBED Equation.DSMT4  (1.11)  EMBED Equation.DSMT4 , B0:8< >1@07>< (1.11) 405B =5A<5I5==CN >F5=:C. 5B>4 K1>@>G=>3> A@54=53> 0AA<>B@8< DC=:F8N  EMBED Equation.DSMT4 . 0AA<>B@8<  EMBED Equation.DSMT4 . 0<5B8<, GB>  EMBED Equation.DSMT4  GB> >?@545;O5B DC=:F8N q(x)  ?;>B=>ABL @02=><5@=>3> @0A?@545;5=8O =0 >B@57:5 [0; 1]. ">340  EMBED Equation.DSMT4  345  EMBED Equation.DSMT4 . (1.12) @8 MB><  EMBED Equation.DSMT4   A;CG09=0O 25;8G8=0, @02=><5@=> @0A?@545;5==0O >B@57:5 [0, 1]. 2545<  EMBED Equation.DSMT4   EMBED Equation.DSMT4  C45< 8A?>;L7>20BL 2 :0G5AB25 >F5=:8 G8A;0 (  EMBED Equation.DSMT4  (1.13) 0==0O >F5=:0 B0:65 O2;O5BAO =5A<5I5==>9. !;CG09=>ABL 8 8<8B0F8O A;CG09=>AB8 AO:89, :B> ?8B05B A;01>ABL : 0@8D<5B8G5A:8< <5B>40< ?>;CG5=8O A;CG09=KE G8A5;, 3@5H5= 2=5 2AO:8E A><=5=89. 6>= D>= 59<0=  40==>< @0745;5 <K :@0B:> :>A=5<AO 8=AB@C<5=B0;L=>3> 0??0@0B0 <5B>4>2 >=B5-0@;>  A;CG09=KE G8A5; 8 A?>A>1>2 8E ?>;CG5=8O. !;CG09=>ABL 8 =5?@54A:07C5<>ABL !;CG09=>ABL  8=B5@5A=59H0O B5<0, @0AA<>B@5=85< :>B>@>9 874@52;5 70=8<0;0AL =5 B>;L:> <0B5<0B8:0, => 8 D8;>A>D8O, B5>;>38O& !C4O ?> 2A5<C, >4=8 87 ?5@2KE 70<5G5==KE ;N4L<8 ?@>O2;5=89 A;CG09=>AB8  MB> 3040=85 8 83@0. 040=85  >?@545;5=85 AC4L1K G5;>25:0 ?> =5:8< <038G5A:8< =04?8AO< 8 A>1KB8O<, 8 :0@B>G=K5 83@K A> 2A5<8 A2>8<8 0B@81CB0<8, =5A><=5==>, O2;ONB A>1>9 O@:85 ?@8<5@K B>3>, :0: A;CG09=>ABL 2 >B;8G85 >B A2>1>4=>3> 2K1>@0 2;8O5B =0 687=L G5;>25:0. 07=8F0 <564C A2>1>4=K< 2K1>@>< 8 >?@545;5==>ABLN 2A5340 O2;O;0AL ?@54<5B>< >65AB>G5==KE A?>@>2 2 D8;>A>D88 8 B5>;>388. %>BO 070@B=K5 83@K 8 3040=85 1K;8 ?@8=OBK C <=>38E :C;LBC@ 8 2> <=>38E AB@0=0E, =0 =8E ?>GB8 2AN4C 4>;3> ACI5AB2>20;> =5:>B>@>5 3;0A=>5 8;8 =53;0A=>5 B01C.  ;CGH5< A;CG05, MB> AG8B0;>AL G5<-B> =5?@8;8G=K<. !:>@55 2A53>, >A=>2>9 B0:>3> >B=>H5=8O O28;8AL F5@:>2=K5 70?@5BK. "5< =5 <5=55, 5I5 0;8;59 8 0@40=> ?8A0;8 ?@> 070@B=K5 83@K 8 ?@>O2;5=85 A;CG09=>AB8, 0 0A:0;L, $5@<0 8 N935=A =0?@028;8 8AA;54>20=8O 2 =0?@02;5=88 A53>4=OH=59 B5>@88 25@>OB=>AB8.  ?5@2CN >G5@54L <0B5<0B8:8 D>:CA8@>20;8 2=8<0=85 =0 AB0B8AB8G5A:>9 A;CG09=>AB8 8 87CG0;8 G0AB>BK ?>O2;5=8O >B45;L=KE M;5<5=B>2 8 1;>:>2 M;5<5=B>2 ?@8 M:A?5@8<5=B0E 2 :0G5AB25 <5@K A;CG09=>AB8. ?>A;54AB288 MB>B ?>4E>4 1K; @0AH8@5= 2 B5>@88 8=D>@<0F88 (?>=OB85 M=B@>?88  <5@K E0>B8G=>AB8 8=D>@<0F88).  60-E 3>40E XX 25:0 <0B5<0B8:8 >;<>3>@>2, %08B8= 8 !>;><>=>DD =57028A8<> 4@C3 >B 4@C30 ?@54AB028;8 206=>5 ?>=OB85, :>B>@>5 8725AB=> :0: >;<>3>@>2A:0O A;>6=>ABL.  ?>8A:0E B>G=>3> 8 C=825@A0;L=>3> >?@545;5=8O 70:>=><5@=>AB8 8 E0>B8G=>AB8 >=8 ?@8H;8 : 2K2>4C, GB> >?B8<0;L=>9 548=8F59 87<5@5=8O A;>6=>AB8 ;N1>9 8=D>@<0F88 O2;O5BAO 4;8=0 =081>;55 :>@>B:>9 ?@>3@0<<K, A?>A>1=>9 35=5@8@>20BL 40==CN 8=D>@<0F8N. !;CG09=>ABL =5 =C6=> ?CB0BL A =5?@54A:07C5<>ABLN. '0ABL A8AB5< <>3CB @0AA<0B@820BLAO :0: A;CG09=K5, => ?@54A:07C5<K5, 0 G0ABL B0:>2K<8 =5 O2;ONBAO. 59AB28B5;L=>, @0AA<0B@820O 45<>3@0D8G5A:CN A8BC0F8N 2 <8@5 8 @>AB ?>?C;OF88 G5;>25G5AB20, <K <>65< AG8B0BL MB>B @>AB A;CG09=K<, E>BO >= 2 F5;>< O2;O5BAO ?@54A:07C5<K<. 0?@>B82, 2@5<O 687=8 8 B>G=>5 2@5<O A<5@B8 :064>3> :>=:@5B=>3> G5;>25:0 O2;O5BAO =5 B>;L:> A;CG09=K<, => 8 =5?@54A:07C5<K<. 5?@54A:07C5<>ABL :@09=5 =5>1E>48<0 2 =5:>B>@KE ?@8;>65=8OE, B0:8E :0:, =0?@8<5@, :@8?B>3@0D8O. 0?@>B82, ?@8 8<8B0F88, :0: ?@028;>, B@51C5BAO ?@54A:07C5<>ABL. >42>4O =5:>B>@K5 8B>38 A:070==><C, =5>1E>48<> >B<5B8BL B>B D0:B, GB> A;CG09=>ABL ?> A59 45=L >AB05BAO A;>6=>9 8 0:BC0;L=>9 ?@>1;5<>9 A>2@5<5==>9 =0C:8, =0E>4OI59 <0AAC ?@8;>65=89 =0 ?@0:B8:5. !;CG09=K5 G8A;0 8 35=5@0B>@K A;CG09=KE G8A5;  2KG8A;5=8OE, 35=5@0B>@K A;CG09=KE G8A5;  CAB@>9AB20, :>B>@K5 35=5@8@CNB MB8 G8A;0 87 =5?@54A:07C5<>3> D878G5A:>3> ?@>F5AA0. >?CAB8<, <K E>B8< >15A?5G8BL =0AB>OICN A;CG09=>ABL ?@8 ?>;CG5=88 G8A5;. 0: MB> A45;0BL? >;CG8BL 8E 87 :0:>3>-B> ?@>F5AA0, :>B>@K9 <K =5 B>;L:> =5 :>=B@>;8@C5< ?>;=>ABLN, => 8 =5 <>65< ?@54A:07K20BL. #AB@>9AB20, 1078@CNI85AO =0 B0:8E ?@>F5AA0E, >1KG=> @01>B0NB A <8:@>A:>?8G5A:8<8 O2;5=8O<8, B0:8<8 :0: B5@<8G5A:89 HC<, D>B>MDD5:B 8;8 :20=B>2K5 O2;5=8O. "5>@5B8G5A:8, MB8 ?@>F5AAK ?>;=>ABLN =5?@54A:07C5<K. 1KG=>, :20=B>2K5 35=5@0B>@K A;CG09=KE G8A5; A>45@60B CA8;8B5;L, :>B>@K9 ?@52@0I05B 2KE>4 D878G5A:>3> ?@>F5AA0 2 =5:>B>@K5 <0:@>A:>?8G5A:85 ?0@0<5B@K, :>B>@K5 <>6=> @538AB@8@>20BL, 8 ?@5>1@07>20B5;L, :>B>@K9 :>=25@B8@C5B 2KE>4 ?@>F5AA0 2 F8D@>2>9 A83=0;. 5=5@0B>@K A;CG09=KE G8A5; <>3CB 1KBL B0:65 ?>;CG5=K 87 <0:@>A:>?8G5A:8E O2;5=89, B0:8E :0:, =0?@8<5@, 83@0;L=K5 :0@BK, 83@0;L=K5 :>AB8, @C;5B:0. E =5?@54A:07C5<>ABL A2O70=0 A B5>@859 =5CAB>9G82KE 48=0<8G5A:8E A8AB5< 8 B5>@859 E0>A0. -B8 B5>@88 CB25@640NB, GB> E>BO <0:@>A:>?8G5A:85 O2;5=8O 8 O2;ONBAO 45B5@<8=8@>20==K<8 2 @0<:0E LNB>=>2>9 <5E0=8:8, @50;L=K5 A8AB5<K @072820NBAO =5?@54A:07C5<> =0 ?@0:B8:5 87-70 =5>1E>48<>AB8 7=0=8O 2A5E =0G0;L=KE CA;>289. 0<5B8< B0:65, GB> MB0 =5>1E>48<0O B>G=>ABL =0G0;L=KE CA;>289 @0AB5B M:A?>=5=F80;L=> A @>AB>< 2@5<5=8. 50;L=K5 D878G5A:85 ?@>F5AAK O2;ONBAO A;>6=K<8, B@C4=> =01;N405<K<8, ?;>E> ?@54A:07C5<K<8. "0:8< >1@07><, 8A?>;L7>20=85 35=5@0B>@>2 A;CG09=KE G8A5; =0 >A=>25 D878G5A:8E ?@>F5AA>2 =0 ?@0:B8:5 A8;L=> 70B@C4=5=>. <5AB> =8E >1KG=> 8A?>;L7CNB B0: =07K205<K5 35=5@0B>@K ?A524>A;CG09=KE G8A5;4. 5=5@0B>@K ?A524>A;CG09=KE G8A5; (PRNG) 5=5@0B>@ ?A524>A;CG09=KE G8A5; (!', PRNG)  0;3>@8B<, 35=5@8@CNI89 ?>A;54>20B5;L=>ABL G8A5;, M;5<5=BK :>B>@>9 ?>GB8 =57028A8<K 4@C3 >B 4@C30 8 ?>4G8=ONBAO 7040==><C @0A?@545;5=8N. 8:0:>9 45B5@<8=8@>20==K9 0;3>@8B< =5 <>65B 35=5@8@>20BL ?>;=>ABLN A;CG09=K5 G8A;0, 0 B>;L:> ;8HL 0??@>:A8<8@>20BL =5:>B>@K5 A2>9AB20 A;CG09=KE G8A5;.  >A:>;L:C :0G5AB2> 8A?>;L7C5<KE A;CG09=KE G8A5; ?@>25@O5BAO A ?><>ILN A?5F80;L=KE B5AB>2, <>6=> =5 8=B5@5A>20BLAO B5<, :0: MB8 G8A;0 ?>;CG5=K: ;8HL 1K >=8 C4>2;5B2>@O;8 ?@8=OB>9 A8AB5<5 B5AB>2. '8A;0, ?>;CG05<K5 ?> :0:>9-;81> D>@<C;5 8 8<8B8@CNI85 7=0G5=8O A;CG09=>9 25;8G8=K, =07K20NBAO ?A524>A;CG09=K<8 G8A;0<8. >4 A;>2>< 8<8B8@CNI85 ?>4@07C<5205BAO, GB> MB8 G8A;0 C4>2;5B2>@ONB @O4C B5AB>2 B0:, :0: 5A;8 1K >=8 1K;8 7=0G5=8O<8 MB>9 A;CG09=>9 25;8G8=K. [ REF _Ref119832462 \r \h 22] 5@2K9 0;3>@8B< 4;O ?>;CG5=8O ?A524>A;CG09=KE G8A5; 1K; ?@54;>65= 6>=>< D>= 59<0=><. = =07K205BAO <5B>4>< A5@548=K :204@0B>2. >OA=8< 53> =0 ?@8<5@5. CABL 7040=> 4-7=0G=>5 F5;>5 G8A;> n1 = 9876. >72545< 53> 2 :204@0B. >;CG8<, 2>>1I5 3>2>@O, 8-7=0G=>5 G8A;> 97 535 376. K15@5< G5BK@5 A@54=85 F8D@K 87 MB>3> G8A;0 8 >1>7=0G8< n2 = 5353. 0B5< 2>72545< 53> 2 :204@0B (28 654 609) 8 A=>20 872;5G5< 4 A@54=85 F8D@K. >;CG8< n3 = 6546. 0;55, 42 850116, n4 = 8501 8 B. 4.  :0G5AB25 7=0G5=89 A;CG09=>9 25;8G8=K ?@54;030;>AL 8A?>;L7>20BL 7=0G5=8O 0,9876; 0,5353; 0,6546; 0,8501; 0,2670; 0,1289 8 B. 4. [ REF _Ref119832462 \r \h 22] > MB>B 0;3>@8B< =5 >?@0240; A51O: ?>;CG0;>AL 1>;LH5 G5< =C6=> <0;KE 7=0G5=89. >MB><C @07=K<8 8AA;54>20B5;O<8 1K;8 @07@01>B0=K 4@C385 0;3>@8B<K. 081>;55 @0A?@>AB@0=5=K ;8=59=K9 :>=3@CM=B=K9 <5B>4, <5B>4 $81>=0GG8 A 70?074K20=8O<8, linear feedback shift registers, generalized feedback shift registers. 7 A>2@5<5==KE !' 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"0:, <K ?>7=0:><8;8AL A> A;54CNI8<8 >A=>2=K<8 ?>=OB8O<8 8 D0:B0<8: AB0B8AB8G5A:>5 <>45;8@>20=85; <5B>4 AB0B8AB8G5A:8E 8A?KB0=89 (<5B>4K >=B5-0@;>); >1I0O AE5<0 <5B>4>2 >=B5-0@;>; >1;0AB8 ?@8<5=5=8O AB0B8AB8G5A:>3> <>45;8@>20=8O; ?@8<5@K ?@8<5=5=8O <5B>4>2 >=B5-0@;>; A;CG09=>ABL; =5?@54A:07C5<>ABL; A;CG09=K5 G8A;0; ?A524>A;CG09=K5 G8A;0; 35=5@0B>@K A;CG09=KE G8A5;; 35=5@0B>@K ?A524>A;CG09=KE G8A5;.  A;54CNI8E @0745;0E <K ?>3>2>@8< >1 MB>< ?>4@>1=55. 8B5@0BC@0 Gamerman, D. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Boca Raton, FL: CRC Press, 1997. Gentle J. Random Number Generation and Monte Carlo Methods. Springer-Verlag NY, 1998. Gilks, W. R.; Richardson, S.; and Spiegelhalter, D. J. (Eds.). Markov Chain Monte Carlo in Practice. Boca Raton, FL: Chapman & Hall, 1996. Gourdon X., Sebah P. ( and its computation through the ages. April 16, 2003. [ HYPERLINK "http://numbers.computation.free.fr/Constants/constants.html" http://numbers.computation.free.fr/Constants/constants.html] Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. New York: Hyperion, pp. 238-239, 1998. Kuipers, L. and Niederreiter, H. Uniform Distribution of Sequences. New York: Wiley, 1974. Manno, I. Introduction to the Monte Carlo Method. Budapest, Hungary: Akadmiai Kiad, 1999. Metropolis N., Ulam S. The Monte Carlo method, J. Amer. statistical assoc., 1949, 44, N247, 335-341. Metropolis, N. "The Beginning of the Monte Carlo Method." Los Alamos Science, No. 15, p. 125. [ HYPERLINK "http://jackman.stanford.edu/mcmc/metropolis1.pdf" http://jackman.stanford.edu/mcmc/metropolis1.pdf] Mikhailov, G. A. Parametric Estimates by the Monte Carlo Method. Utrecht, Netherlands: VSP, 1999. Niederreiter, H. and Spanier, J. (Eds.). Monte Carlo and Quasi-Monte Carlo Methods 1998, Proceedings of a Conference held at the Claremont Graduate University, Claremont, California, USA, June 22-26, 1998. Berlin: Springer-Verlag, 2000. Sobol, I. M. A Primer for the Monte Carlo Method. Boca Raton, FL: CRC Press, 1994. Weisstein Eric W. "Monte Carlo Method." From MathWorld  A Wolfram Web Resource. [ HYPERLINK "http://mathworld.wolfram.com/MonteCarloMethod.html" http://mathworld.wolfram.com/MonteCarloMethod.html] >;LH0O !>25BA:0O -=F8:;>?548O. 740=85 3-5. ., !>25BA:0O M=F8:;>?548O, 1970. CA;5=:> .., >;5=:> .., !>1>;L .., !@03>28G .., (@50F845@ ... 5B>4 AB>E0AB8G5A:8E 8A?KB0=89 (<5B>4 >=B5-0@;>). .: $, 1962. CA;5=:> .., (@5945@ ... 5B>4 AB0B8AB8G5A:8E 8A?KB0=89 >=B5-0@;> 8 53> @50;870F8O 2 F8D@>2KE <0H8=0E. $87<0B387, 1961. <C@<0= .. "5>@8O 25@>OB=>AB8 8 <0B5<0B8G5A:0O AB0B8AB8:0. .: KAH0O H:>;0, 1977. @<0:>2 !. . 5B>4 >=B5-0@;> 8 A<56=K5 2>?@>AK. ., 1971. @<0:>2 !.., 8E09;>2 .. !B0B8AB8G5A:>5 <>45;8@>20=85. : 0C:0, 1982. @<0:>2 !.., 8E09;>2 .. C@A AB0B8AB8G5A:>3> <>45;8@>20=8O. .:0C:0, 1976. @0<5@ .. 0B5<0B8G5A:85 <5B>4K AB0B8AB8:8. : 8@, 1975. !>1>;L .. '8A;5==K5 <5B>4K >=B5-0@;>. .:0C:0, 1973. "5?;O:>2 . >45;8@CO 687=L // Hard n soft, !8, 2001. [ HYPERLINK "http://www.hardnsoft.ru/magazine.php?issue=86&article=18&page=2" http://www.hardnsoft.ru/magazine.php?issue=86&article=18&page=2]  0<5B8< 4;O ;N1>?KB=KE G8B0B5;59, GB> :0: A?@0254;82> ?>4G5@:=C; 2 A2>59 :=835 [ REF _Ref119832462 \r \h -21] .. !>1>;L, <5B>4 >=B5-0@;> =8:0: =5 ?><>305B 2K83@K20BL 2 @C;5B:C 8 2>>1I5 =5 8<55B : MB><C =8:0:>3> >B=>H5=8O!  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