Pivato Marcus - Stochastic Processes and Stochastic Integration.pdf - Stochaistic Processes and Differential Equations - Kuya

!" # $

M æM

9;:=<?>A@CBED.FHGJI.KMLN<?>OK;BPLRQTSUB BEVCW ” ÷ g qcs zre ƒ g q'z-gik+z^nFk9nVgie#¨)k ‡ ‚ k+m n q'z"m#¤'qczrk+m_‡ ¯Ÿ m_siprqce_z b

”…z^s gik9m_n NX ^giprqts nreZv{wrxyk{z-g|qts|nFqc˙Zqcnrk+n qcz g ‚ eosixym_¤'¤ YX 6sik{xyq' ì \qcz^nFk+‹6k+z^nFk+z g [Z xyeFnFwr¤ck+s ]\

e ƒ¯À gik{ Ô Zg+bºj#m ƒ giprk+‡Vgip^m_z ¨)k{qczr Ø m_‡i‡«m ƒ zr Ø k+n¥qcz Õ m†¤'qczrk+m_‡3e_‡«nFk{‡ EX g ‚ prk+sikyxeFnFw^¤'k9s$m ƒ ‡ ‚ k

m ƒ ‡ ‚ ‡«m ƒ zr Ø k+nØq'z’m¸¤ceZe sik ’ prk+q'‡«m ƒ ‡«v«pZ·¸e_ ¯ ^Z ¤ce_ Ø qcv+m ƒ ¤ nrk{‹)k{z^nFk+z^v · H\‘_ 3xeFnFw^¤'k9s†nrk+m ƒ ¤cqczr Ø

flq'gip¢xye_‡ ‚ kom nF˙Xm ƒ z^v{k+n gie ‹rqtv{s e ƒ¯ –gik+z¸nFk+‹6k+z^n Õ wr‹)e_z Õ g ‚ prk†‡ik9m_nFk+‡+ ç s3˘ZzreXfl¤ck+nF Ø ke ƒ¯

xmXg ‚ k{‡ ‚ qcm_¤ v eX˙ k{‡ ‚ k+nØqczhv k+‡ g«m ƒ qcz ‹r‡ ‚ k{˙Zq'e w^sºxyeFnFwr¤ck+s+b a prk{z siw^v«p@‡ ‚ k{¤tmXg ‚ q'e z^siprq'‹6s

e ƒ¯À ¤'e Ø _qtv{m_¤/nrk{‹)k{z^nFk+z^v · ’ k Ô Fqcs g X giprk+·flq'¤c¤ Â ¨)kyk Ô F‹r¤cqcv{q ° g ‚ ¤'·qcz^nFqtv{m ƒ gik9n ’ qcz giprky¤cqcs g3e ƒ¯

U › W-UXW =c ž 5⁄+ žŸ™ +WZ⁄ flprqtv«p†m_‹r‹)k+m ƒ ‡#m ƒ gDgiprk3¨)k{ Ø q'zrz^q'zr Ø e_ ¯ k9m_v«p†xeFnFw^¤'k b

¯¥eFnFwr¤ck+sVm_¤csie†sie_xyk{giqcxk9sVp^m › ˙_k ]_ š 6UXW dc žŸ ⁄9 žÒ™ 9WZ⁄ b§Dprk+sikm ƒ ‡ ‚ k e_giprk+‡ xyeFnFwr¤ck+s

flprqtv«p eX 6m_¤ ° g ‚ pre_w^ Ø _p zre ƒ g ¤'e Ø _qtv{m ƒ ¤c¤c· KfIUDUIg>U>hQPigj ¯Ò e ‡|v e xy‹r‡ik+prk{z6nFq'z^ Ø ygiprk$xm ƒ gik{‡ ‚ qtm ƒ ¤ qcz

wrk+s giqce_z RX _xm › ·"¨)klprk{¤c‹F ¯Ò wr¤)qcz‹^‡ieX˙ZqtnFq'z^ Ø Vm_zyq'z-giw^q ° g ‚ q'˙ k|v e z g ‚ k Ô Zg Â e_‡<xye_giqc˙ › m ƒ giqce_zy ¯Ò e ‡

flp^m ƒ g#qcs#nrqcs ‚ v w^s ‚ sik+n b Â d|k{z^v{k CX ^q' ¯ /xeFnFw^¤'k"˝ ü qts#m l i]I.imIUnhFH<?>g<oLpI ¯Ò e_‡lxyeFnFwr¤ck"¿ qX Fgiprk+z

xyeFnFwr¤ck ˝’s p^e_wr¤tnº¨)k ‡ ‚ k+m n NX -wrz^nFk+‡ ‚ s gieZeFn NX Fm ƒ z^noxm_s gik{‡ ‚ k+nº¨-·g ‚ prk s giw6nFk{z-gD¨6k{ ¯Ò e_‡ ‚ k

xyeFnFwr¤cko¿ qts$m ƒ ‹^‹r‡ie-m_v«prk9n b” ÷¯ DxeFnFw^¤'ko˝ıqcs X qcz^s gik+m n NX /m D]BrimIUn.FH<?>g<oLsI X gip^k{z gip^k

‡ ‚ k+m_nrk{‡#qts m nF˙Zqcsik+n ÕíŸ ¨rwFgVzre ƒ g xym_z^nrm ƒ gik+n6 î Dgie1‡ik9m_n e ‡|¨r‡ ‚ eXf#s k$˝Ns qcx"w^¤ ° g«m ƒ zrk+e_w^si¤'·

§Dprk ™ +[ Ht u Ÿ W Úš 6Y] š 6 ˜ C ™ 9WZ ˜ C ™ +⁄ ‹)e_‡igi‡«m › ·Zs†m ƒ z e_‡ ‚Ø m ƒ z^qcs ‚ mXg ‚ q'e z^m ƒ ¤ siv«prk+xm¢flprk+‡ik+¨-·

xyeFnFwr¤ck+sm ƒ ‡ ‚ kºnFq'˙ZqtnFk+n¢q'z-gie vZ iv«p^m_‹Fgik+‡ ‚ s ]\wXqZ isik+v giqce_z^s ]\ ¥m ƒ z^n xZ ‚ s w^¨^s k9v‰g ‚ q'e z^s m\ ^b¥§Dprqcs

e_‡ ‚Ø m_zrqtsim ƒ giqce_z^m_¤)s ‚ v«prk{xmqtsDw^s k{ ¯Ò wr¤ ¯Ò e ‡l Ø _‡ ‚ e_wr‹rqczr Ø y‡ ‚ k{¤tmXgik9noxm ƒ gik{‡ ‚ qtm ƒ ¤Cgie Ø _k{giprk+‡ X Z¨rwFg

e_z6v k|m_ Ø m ƒ qcz eX q ° g À qcs zre ƒ g q'z-gik+z^nFk9nygies wr ØØ _k9s µ g m_z-·ysie_‡ig e ƒ¯ ¤cq'zrk9m ƒ ‡ ¤'e Ø _qtv{m ƒ ¤)s µ g ‚ ‡iw6v‰giw^‡ik b