˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔೖ໳ ٻΊΒΕΔഎܠͱϓϥΠόγʔอޢͷ࢓૊Έ ∁ڮཌྷ c5TVCBTB 5",")"4)* -*/&Ϡϑʔݚڀॴ ্੮ݚڀһ "*4FDVSJUZ1SJWBDZਪਐࣨ ࣨ௕

˜-:$PSQPSBUJPO 5TVCBTB 5",")"4)* 1I% IUUQTXXXOFDTPMVUJPOJOOPWBUPSTDPKQTMEBOPOZ /&$ -*/& -*/&Ϡϑʔ 4#*OUVJUJPOT d d /&$σʔλಗ໊ԽιϦϡʔγϣϯ ʮ-*/&ʯΞϓϦͷελϯϓαδΣετ ࿈߹ֶशࠩ෼ϓϥΠόγʔ IUUQTMJOFDPSQDPNKB TFDVSJUZBSUJDMF ੜ੒"* ετϨε ςετ"* ҙਤతͳ߈ܸతΫΤϦ 8BUFSNBSL %JGGVTJPO.PEFM --.ͷετϨεςετ ఢରతಁ͔͠ʹΑΔஶ࡞ݖอޢ $.6d ໦ߋ௡ߴઐ ஜ೾େֶ

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔͱ͸ʢ֓ཁʣ ౷ܭ։ࣔʹ͓͚ΔϓϥΠόγʔϦεΫ ࠩ෼ϓϥΠόγʔͷ࢓૊Έ ຊߨٛͷίϯςϯπ ࠩ෼ϓϥΠόγʔͷৄࡉͳཧ࿦΍Ԡ༻ΑΓ΋ɺͳͥࠩ෼ϓϥΠόγʔ͕ඞཁͱ͞Ε͍ͯΔ͔ʹয఺Λ౰ͯ·͢

˜-:$PSQPSBUJPO 1SJWBDZ&OIBODJOH5FDIOPMPHJFT 1&5T 1&5Tʹ͸ɺ ҉߸౳ʹΑΔΞΫηε੍ޚٕज़ͱ ৘ใͦͷ΋ͷΛՃ޻͢Δٕज़ ͕͋Δ ࿈߹ֶशɾ ہॴࠩ෼ϓϥΠόγʔ ಗ໊Խɾσʔλ߹੒ ࠩ෼ϓϥΠόγʔ ੺͍఺ઢΑΓࠨଆ͕ϓϥΠόγʔอޢͷൣғ FHಗ໊Խ΍ࠩ෼ϓϥΠόγʔ FH࿈߹ֶश΍ൿີܭࢉ

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔͱ͸ ϊΠζʢ ʣ͕Ճࢉ͞Ε͍ͯΔͱϓϥΠόγʔอޢ͞Ε͍ͯΔΑ͏ʹײ͡·ͤΜ͔ʁ ౷ܭత ͳग़ྗ ϊΠζ ΛՃࢉ 𝜖 ∞ TUSPOH XFBL ʜ ࠩ෼ϓϥΠόγʔ͕ఏڙ͢Δ΋ͷ • ϊΠζͷՃࢉʹର͢Δ ཧ࿦తͳϓϥΠόγʔอޢͷई౓ • ॴఆͷϓϥΠόγʔڧ౓ 𝜖 ͷ ୡ੒ʹඞཁͳϊΠζͷಋग़

˜-:$PSQPSBUJPO ͭͷओཁͳϓϥΠόγʔϞσϧ $FOUSBM %JGGFSFOUJBM1SJWBDZ -PDBM%JGGFSFOUJBM1SJWBDZ ୈࡾऀ΁ͷ ౷ܭ஋ͷެ։ ػඍͳ ౷ܭͷऩू αʔόʔΛ ৴༻͠ͳ͍ αʔόʔΛ ৴༻͢Δ ಋೖࣄྫ • $ISPNFϒϥ΢βͰͷ౷ܭऩू (PPHMF • J04σόΠεͰͷ౷ܭऩू "QQMF • ελϯϓαδΣετͷ࿈߹ֶश -*/&Ϡϑʔ ಋೖࣄྫ • ೥౓ถࠃࠃ੎ௐࠪ 64$FOTVT • 'VMM63-TEBUBTFU .FUB • /FYUXPSEQSFEJDUJPOJO(CPBSE (PPHMF • "VEJFODF&OHBHFNFOU"1* -JOLFE*O ʢ͝ࢀߟʣ"MJTUPGSFBMXPSMEVTFPGEJGGFSFOUJBMQSJWBDZIUUQTEFTGPOUBJOFTQSJWBDZSFBMXPSMEEJGGFSFOUJBMQSJWBDZIUNM

˜-:$PSQPSBUJPO 64$FOTVTͰࠩ෼ϓϥΠόγʔΛར༻ͨ͠ཧ༝ • ࠩ෼ϓϥΠόγʔ͸ɺࠓ೔ͷϓϥΠόγʔڴҖʹର͢Δ ࠷৽ͷηʔϑΨʔυͰ͋Δ • εύίϯ͸ɺݸਓ৘ใΛಛఆ͢ΔͨΊʹෳ਺ͷ%#͔Β σʔλΛݟ͚ͭग़͠ɺর߹͢Δ͜ͱͰɺ܈ऺͷத͔Β͋ ͳͨΛ༰қʹબͼग़͢ʢڱ͍஍ҬʹॅΜͰ͍ͯɺྡਓͱ ਓछ΍ຽ଒͕ҟͳΔ৔߹͸ಛʹʣ • ϓϥΠόγʔʹର͢ΔਂࠁͳڴҖ͸ɺ೥લͷࠃ੎ௐࠪ ͷ࣌ʹ͸ଘࡏ͠ͳ͔ͬͨ΋ͷͰ͋Δ • ࢲͨͪ͸ɺਓʑͷϓϥΠόγʔΛอޢ͠ଓ͚ΔͨΊʹɺ ৽͍ٕ͠ज़Λ࢖Θͳ͚Ε͹ͳΒͳ͍ • ࠓ೔ͷϓϥΠόγʔͷڴҖͷن໛Λߟ͑Δͱɺաڈͷํ ๏͸ɺެද͞Εͨσʔλʹஶ͘͠େ͖ͳ࿪ΈΛੜͤ͡͞ɺ σʔλͷଟ͘Λ࢖༻Ͱ͖ͳͯ͘͠͠·͏ͩΖ͏ IUUQTXXXDFOTVTHPWDPOUFOUEBN$FOTVTMJCSBSZGBDUTIFFUTEJGGFSFOUJBMQSJWBDZBOEUIFDFOTVTQEG

˜-:$PSQPSBUJPO Ҏ߱ͷύʔτͷૂ͍ • աڈʹى͖ͨϓϥΠόγʔ৵֐ͷࣄྫͱɺͦ͜Ͱར༻͞ΕͨϓϥΠόγʔอޢٕज़ʹ͍ͭͯ ঺հ͠·͢ • աڈࣄྫΛ௨ͯ͠ɺͳͥࠩ෼ϓϥΠόγʔ͕ඞཁͳͷ͔ɺΛղઆ͍͖ͯ͠·͢ • ݫີͳఆٛΑΓ΋ɺΘ͔Γ΍͢͞Λ༏ઌͨ͠આ໌Λ͠·͢

˜-:$PSQPSBUJPO ౷ܭ։ࣔʹ͓͚ΔϓϥΠόγʔϦεΫ

˜-:$PSQPSBUJPO ถࠃ."भʹ͓͚Δ࠶ࣝผͷ໰୊ ೥୅ • ถࠃ."भͰ͸ɺभͷ৬һͷ௨Ӄه࿥ " Λر๬͢Δݚڀऀʹެ։ ໊લ͸࡟আ • έϯϒϦοδࢢͷ༗ݖऀσʔλϕʔε # ͸υϧͰߪೖͰ͖ͨ • " ͱ # ͷ૊Έ߹Θ͔ͤΒ8FME஌ࣄͷϨίʔυ͕؆୯ʹಛఆͰ͖ͨ (FOEFS ;JQ #JSUI %JTFBTF ' B YYBBCC "#$ . C YYZZ[[ %&' . D BCXXUU ()* ' E NOQQRR +,- /BNF (FOEFS ;JQ #JSUI ʜ ' B YYBBCC 8JMMJBN8FME . C YYZZ[[ . D BCXXUU ' E NOQQRR /BNF (FOEFS ;JQ #JSUI %JTFBTF ' B YYBBCC "#$ 8JMMJBN8FME . C YYZZ[[ %&' . D BCXXUU ()* ' E NOQQRR +,- +0*/ ४ࣝผࢠ 2VBTJ*EFOUJGJFS2*%

˜-:$PSQPSBUJPO /FUGMJY1SJ[Fͷ࠶ࣝผͷ໰୊ • ಗ໊Խ͞Ε͍ͯͳ͍֎෦ͷσʔλϕʔε *.%# ͱͷಥ߹ʹΑͬͯɺಗ໊Խ͞Ε͍ͯͨίϝ ϯτͱϢʔβ͕ରԠ෇͍ͯ͠·ͬͨ • ίϝϯτʹ͸੓࣏৴৚͕Θ͔Δ΋ͷ΋͋ͬͨ • ݸͷධՁͱ೔෇ िؒҎ಺ͷਫ਼౓ ͕෼͔Ε͹ͷਫ਼౓ͰݸਓΛಛఆͰ͖ͨ 6TFSOBNF 5JUMF 3BUF "MJDF """ ### %%% #PC """ 999 1TFVEP*% 5JUMF 3BUF $PNNFOU Y """ ### %%% *UTFFNTYYY B ::: 999 "OPOZNJ[FE/FUGMJY.PWJFSBOLJOHEBUB /POBOPOZNPVT*.%#NPWJFSBUJOH +0*/

˜-:$PSQPSBUJPO Lಗ໊Խ • ಗ໊Խɿσʔλͷಛఆ΍ࣝผΛࠔ೉ʹ͢ΔͨΊʹߦ͏σʔλͷՃ޻ॲཧ • Lಗ໊Խɿ%#಺ʹɺ೚ҙͷϨίʔυͱಉ͡४ࣝผࢠͷ૊Λ࣋ͭଞͷϨίʔυ͕Lݸଘࡏ • ४ࣝผࢠ 2VBTJ*EFOUJGJFS ɿ૊߹ͤʹΑͬͯݸਓΛࣝผ͠ಘΔଐੑͷू߹ɻࣄલʹఆٛ "HF (FOEFS 4BMBSZ "MJDF 'FNBMF . #PC .BMF . $IBSMJF .BMF . %BWJE .BMF , &NNB 'FNBMF . 'SBOD .BMF . (FPSHF .BMF , )BOB 'FNBMF , "HF (FOEFS 4BMBSZ . . . , . . , , Lಗ໊Խ L

˜-:$PSQPSBUJPO Lಗ໊Խͷݶք • ४ࣝผࢠҎ֎ͷଐੑʹର͢Δ֎෦஌ࣝͷಥ߹ʹΑΓɺLಗ໊ԽΛഁΒΕΔ͜ͱ͕͋Δ • è ߈ܸऀͷഎܠ஌ࣝʹΑͬͯ͸ಗ໊ੑ͕े෼Ͱͳ͍ "HF (FOEFS 4BMBSZ . . . , . . , , Lಗ໊Խ L "HF (FOEFS 1IPOF "MJDF 'FNBMF #PC .BMF $IBSMJF .BMF %BWJE .BMF &NNB 'FNBMF 'SBOD .BMF (FPSHF .BMF )BOB 'FNBMF (FOEFS 4BMBSZ #PC .BMF . &NNB 'FNBMF . (FPSHF .BMF , ᶃ ᶃ ᶄ 'SBODà 4BMBSZ. ΛಛఆͰ͖ͯ͠·͏ ఢରऀͷ֎෦஌ࣝ

˜-:$PSQPSBUJPO ࠩ෼߈ܸ • ෳ਺ͷ౷ܭ৘ใͷʮࠩ෼ʯ͔Βಛఆͷݸਓʹؔ͢Δ৘ใΛਪఆ • ಉ͡ϢʔβΛؚΉσʔλϕʔε͔Βੜ੒ͨ͠ෳ਺ͷ౷ܭ৘ใ͕ର৅ BWHTBMBSZ ສԁ BWHTBMBSZ ສԁ ʲ2VJ[ʳ"MJDFͷ೥ऩ͸ʁ ʜ ʜ ʜ ʜ "MJDF "MJDF͕ୀ৬ FOHJOFFST FOHJOFFST ೥ ೥

˜-:$PSQPSBUJPO 2VJ[ͷճ౴ BWHTBMBSZ ສԁ BWHTBMBSZ ສԁ ʲ2VJ[ʳ"MJDFͷ೥ऩ͸ʁ ʜ ʜ ʜ ʜ "MJDF "MJDF͕ୀ৬ FOHJOFFST FOHJOFFST ೥ ೥ Yr Y ສԁ ౴͑

˜-:$PSQPSBUJPO ࠩ෼߈ܸͷࣄྫ • 'BDFCPPLͷ1**CBTFE5BSHFUJOH ݱࡏ͸मਖ਼ࡁΈ • ޿ࠂλʔήςΟϯάͷޮՌΛܭଌ͢ΔͨΊͷ౷ܭ෼ੳ"1* • ։੍ࣔޚͷͨΊʹᮢ஋ʹΑΔอޢΛಋೖ͍͕ͯͨ͠ɺόΠύε͞Εͨ • ి࿩൪߸΍ϝʔϧΞυϨεɺ8FCӾཡཤྺ͕࿙Ӯ IUUQTXXXZPVUVCFDPNXBUDI W-Q *X:WY(QL IUUQTXXXGUDHPWTZTUFNGJMFTEPDVNFOUTQVCMJD@FWFO UTQQSJWBDZDPONJTMPWF@QEG

˜-:$PSQPSBUJPO σʔλϕʔε࠶ߏங߈ܸ • ౷ܭ৘ใͷݩʹͳͬͨϨίʔυΛ༷ʑͳެ։৘ใΛۦ࢖ͯ͠෮ݩ l਺ಠzΛղ͘Πϝʔδ "O&YBNQMF IUUQTXXXDFOTVTHPWBCPVUUSBJOJOHXPSLTIPQTEBTQSFTFOUBUJPOQEG ౷ܭ৘ใͷಋग़աఔʹ͸ɺ ϧʔϧɺΞϧΰϦζϜɺґଘؔ܎͕͋Δ

˜-:$PSQPSBUJPO σʔλϕʔε࠶ߏங߈ܸͷࣄྫ • ถࠃͷ೥ͷࠃ੎ௐࠪ • Ҏ্ͷݸਓͷϨίʔυ͕෮ݩ͞ΕಘΔ͜ͱ͕ใࠂ͞Ε͍ͯΔ IUUQTXXXDFOTVTHPWBCPVUUSBJOJOHXPSLTIPQTEBTQSFTFOUBUJPOQEG ೥ͷถࠃͷࠃ੎ௐࠪͰ͸ࠩ෼ϓϥΠόγʔ͕ಋೖ͞Ε͍ͯΔ

˜-:$PSQPSBUJPO ౷ܭͷ҆શͳ։ࣔ r ස౓ͱࠩ෼ͷ͖͍͠஋ॲཧ • ݪཧతʹ͸Մೳ͕ͩɺ͋Γͱ͋ΒΏΔࠩ෼ΛຖճνΣοΫ͢Δ͜ͱ͸༰қͰ͸ͳ͍ • ͖͍͠஋ॲཧʹΑͬͯɺར༻ෆՄೳʹͳΔσʔλ͕ଟ਺ੜ͡ΔڪΕ ೥୅ ੑผ ਓ਺ ୅ உ ୅ ঁ ୅ உ ୅ ঁ ೥୅ ੑผ ਓ਺ ୅ உ ୅ ঁ ୅ உ ୅ ঁ ೥୅ ੑผ ਓ਺ ୅ உ ୅ ঁ ୅ உ ୅ ঁ ਓ਺ͷ͖͍͠஋ɿ ࠩ෼ͷ͖͍͠஋ɿ /( 0, ࣌ࠁ 5 ࣌ࠁ 5𝜏 ݁ୗऀΛूΊΒΕͳ͍ఔ౓ʹ େ͖͍͖͍͠஋Λઃఆ ྫ

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔ͕ٻΊΒΕ͍ͯΔഎܠ L ಗ໊Խͷݶք • ֎෦஌ࣝʹ੬ऑ ɿ֎෦஌ࣝͱͷಥ߹ʹΑͬͯɺಗ໊Խ͕ഁΒΕΔڪΕ • ෳ਺ެ։ʹඇରԠɿෳ਺ͷಗ໊Խσʔλͷಥ߹ʹΑͬͯ΋ɺಗ໊Խ͕ഁΒΕΔڪΕ • ༗༻ੑҡ͕࣋ࠔ೉ɿσʔλͷෳࡶ౓ɺڴҖͷڧ͞ʹԠͯ͡༗༻ੑͷҡ͕࣋ΑΓࠔ೉ʹ ৽͍͠ڴҖͷొ৔ • ࠩ෼߈ܸ • σʔλϕʔε࠶ߏங߈ܸ ౷ܭσʔλ΍ػցֶशϞσϧʹର͢ΔϓϥΠόγʔई౓ͷඞཁੑ

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔͷ࢓૊Έ

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔͱ͸ ϊΠζʢ ʣ͕Ճࢉ͞Ε͍ͯΔͱϓϥΠόγʔอޢ͞Ε͍ͯΔΑ͏ʹײ͡·ͤΜ͔ʁ ౷ܭత ͳग़ྗ ϊΠζ ΛՃࢉ 𝜖 ∞ TUSPOH XFBL ʜ ࠩ෼ϓϥΠόγʔ͕ఏڙ͢Δ΋ͷ • ϊΠζͷՃࢉʹର͢Δ ཧ࿦తͳϓϥΠόγʔอޢͷई౓ • ॴఆͷϓϥΠόγʔڧ౓ 𝜖 ͷ ୡ੒ʹඞཁͳϊΠζͷಋग़

˜-:$PSQPSBUJPO %1ʹ౷ܭॲཧͱϊΠζՃࢉʹΑΔग़ྗͷࣝผࠔ೉ੑ • ग़ྗͷࣝผࠔ೉ੑɿೖྗͷΘ͔ͣͳࠩҟʹґΒͣग़ྗ͕΄ͱΜͲมΘΒͳ͍ • ˞Ұൠతͳʮಗ໊Խʯͱ͸ҟͳΔϓϥΠόγʔͷߟ͑ํ • ॴఆͷࣝผࠔ೉ੑΛୡ੒͢ΔΑ͏ʹϝΧχζϜℳʢ౷ܭॲཧͱϊΠζՃࢉʣΛઃܭ ℳ ℳ ग़ྗ஋ ग़ ྗ ֬ ཰

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔͷ࢓૊Έ • %1ʹΑΔϓϥΠόγʔอޢʹϢʔβʔͷߩݙ˞Λ੍ݶ͠ɺϊΠζͰߩݙͷ༗ແΛ෴͍Ӆ͢ • ˞Ϣʔβʔͷߩݙɿग़ྗʢ౷ܭ৘ใʣʹର͢Δ̍ݸਓʢσʔλʣͷد༩ͷେ͖͞ ߩݙͷ੍ݶ ʢ&ODPEFʣ ू໿ ʢ"HHSFHBUFʣ "MJDF #PC $IBSMJF ઁಈ ʢ1FSUVSCʣ ສԁ ສԁ ສԁ ສԁ ສԁ ສԁ ສԁ 0 1000 2000 3000 4000 5000

˜-:$PSQPSBUJPO 𝝐, 𝜹 %JGGFSFOUJBM1SJWBDZ ϝΧχζϜ ℳ: 𝒟 → 𝒮 ͕ 𝜖, 𝛿 %1Λຬͨ͢ͱ͸ɺྡ઀σʔλϕʔε 𝐷, 𝐷" ∈ 𝒟 ͓Αͼ೚ҙͷग़ྗͷू߹ 𝑆 ⊆ 𝒮 ʹରͯ͠ҎԼ͕੒Γཱͭͱ͖Ͱ͋Δ %BUBCBTF𝑫 0VUQVU 𝜖 ∞ TUSPOH XFBL ʜ Pr ℳ 𝐷 ∈ 𝑆 ≤ exp 𝜖 Pr ℳ 𝐷! ∈ 𝑆 + 𝛿 ℳ 𝑫′ɿ BEKBDFOUPG𝑫 ℳ 𝜖 ≥ 0, 𝛿 ∈ 0,1 ) ೖྗ͕มԽͯ͠΋ग़ྗʹ͸΄ͱΜͲʢexp 𝜖 ఔ౓͔͠ʣӨڹ͕ͳ͍ %XPSL%JGGFSFOUJBMQSJWBDZ*$"-1

˜-:$PSQPSBUJPO -BQMBDFϝΧχζϜ ࠷΋Α͘஌ΒΕͨϥϯμϜԽॲཧΛ࣮ݱ͢ΔϝΧχζϜʢ𝛿 = 0Λ૝ఆʣ ℳ 𝐷 = 𝑓 𝐷 + Lap 0, Δ. 𝜖 -BQMBDF.FDIBOJTN 𝜖 = 10, Δ! = 1 𝜖 = 1, Δ! = 1 ฏۉɿ ඪ४ภࠩɿ 2 "! # ͷ ϥϓϥε෼෍͔ΒϊΠζΛαϯϓϦϯά Δ' = sup (,(!∈𝒟 𝑓 𝐷 − 𝑓 𝐷" , ℓ𝟏 TFOTJUJWJUZ Δ-./01 = 1 Δ2340 = 1 𝑛 ˞૝ఆ͢Δྡ઀%#ʹґଘ &Y 4FOTJUJWJUZ𝚫𝒇 ೚ҙͷҰϨίʔυͷมԽ˞͕ؔ਺ͷग़ྗʹӨڹΛ༩͑Δ౓߹͍ %XPSL%JGGFSFOUJBMQSJWBDZ*$"-1

˜-:$PSQPSBUJPO ࠩ෼ϓϥΠόγʔͷ࣮૷ ώετάϥϜʹ-BQMBDFϝΧχζϜΛద༻͢Δྫ ϓϥΠόγʔϞσϧ • อޢ୯Ґɿ6TFSMFWFM Ϩίʔυਓ • ྡ઀%#ɿBEESFNPWBM

˜-:$PSQPSBUJPO -BQMBDFϝΧχζϜͷڍಈ ϥϯμϜੑΛ࣋ͬͨڍಈΛ͢ΔͨΊɺಉ͡ઃఆͰ΋ຖճग़ྗ͕ҟͳΔ 𝜖 = 1, Δ# = 1 𝜖 = 1, Δ# = 1 𝜖 = 1, Δ# = 1

˜-:$PSQPSBUJPO -BQMBDFϝΧχζϜͷڍಈ ϓϥΠόγʔύϥϝʔλ𝜖Λมಈʢ𝜖খ à ϓϥΠόγʔอޢڧʣ 𝜖 = 0.1 𝜖 = 0.5 𝜖 = 2 𝜖 = 0.05 𝜖 = 10 Δ# = 1

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˜-:$PSQPSBUJPO ·ͱΊ • աڈͷϓϥΠόγʔ৵֐ͷࣄྫͱطଘͷϓϥΠόγʔอޢٕज़ʹ͍ͭͯ঺հ • աڈࣄྫΛ௨ͯ͠ɺͳͥࠩ෼ϓϥΠόγʔ͕ඞཁͳͷ͔ɺΛղઆ • ࠩ෼ϓϥΠόγʔͷಋೖɾਁಁɾීٴʹ͓͚Δ՝୊Λ঺հ • ݫີͳఆٛΑΓ΋ɺΘ͔Γ΍͢͞Λ༏ઌͨ͠આ໌Λ͠·ͨ͠ • ػցֶशʹؔ͢Δ࿩୊ʹ͍ͭͯ͸࣌ؒͷؔ܎ͰׂѪ͠·ͨ͠

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