Description Usage Arguments Value Examples
Create a Wiener Process
1 | wiener.process(dispersion = 1)
|
dispersion |
the dispersion parameter of the Wiener process. |
a function hanlde in the form of X(tObs,n)
which generates n
independent trajectories observed at tObs
.
1 2 | X <- wiener.process()
X(regular.grid(50),25)
|
[,1] [,2] [,3] [,4] [,5]
[1,] -0.071450816 0.009027217 0.1432459256 0.203801977 0.465198402
[2,] 0.061686957 -0.011421017 -0.1096963564 0.053198693 0.031780900
[3,] 0.090651142 0.154471294 0.0003794077 -0.191587883 -0.216844551
[4,] 0.021229718 0.056959932 -0.2818211219 -0.158271474 -0.087836611
[5,] -0.049354155 -0.171794822 -0.2530741532 -0.356919365 -0.369566453
[6,] -0.019726521 -0.011346904 -0.0072709485 -0.129311179 -0.140683653
[7,] -0.075250926 -0.030124241 0.0250866225 0.007779742 -0.059174848
[8,] 0.075998031 0.058351399 0.0759700748 -0.053402391 -0.118481385
[9,] -0.119235436 -0.231819096 -0.2072066097 -0.008390118 -0.135062934
[10,] -0.059991970 -0.080399179 0.0069902119 -0.098059511 -0.041064710
[11,] 0.034070177 0.061719283 0.1391211222 0.219461336 0.135798123
[12,] 0.017441618 0.138006314 0.0832739767 -0.019599183 0.054874320
[13,] 0.022620886 0.003860571 -0.0996388751 -0.004220876 0.005680206
[14,] 0.109546165 0.097944362 0.1415852968 0.124716924 0.067995809
[15,] 0.014060865 0.105728212 0.0527148147 -0.069154385 -0.105715864
[16,] 0.120974639 0.062930512 0.1671867964 0.132017881 0.044187488
[17,] -0.045559612 -0.275981102 -0.4041038082 -0.448352358 -0.463967951
[18,] 0.065065252 0.154558563 0.0866629043 -0.065064553 -0.030173139
[19,] -0.038312650 -0.161573489 -0.2405786436 -0.176757240 -0.122916131
[20,] 0.006335704 -0.021952011 0.0271737877 -0.014044189 -0.112877514
[21,] 0.106659036 0.275470092 0.2816785994 0.124874567 0.146235825
[22,] -0.004219157 -0.139788344 -0.2599323508 -0.149558379 -0.151904690
[23,] 0.131507141 0.133207237 0.0992895174 0.152934493 0.199511128
[24,] 0.044851491 -0.041524231 -0.0376700035 0.024629765 0.120781533
[25,] 0.071382409 0.107779195 -0.1202576254 -0.081310266 -0.119231972
[,6] [,7] [,8] [,9] [,10] [,11]
[1,] 0.405409836 0.087857205 0.09592975 0.19801815 0.22392395 0.13435879
[2,] 0.046657229 -0.016738858 -0.04109859 0.04813712 0.16860957 0.08768127
[3,] -0.436079490 -0.453751686 -0.31179116 -0.20579061 -0.05653499 -0.09224046
[4,] -0.229009261 -0.339234240 -0.49940484 -0.56567136 -0.35028827 -0.26968614
[5,] -0.391752945 -0.526877720 -0.56217712 -0.56659217 -0.68047694 -0.73512207
[6,] -0.256600676 -0.314193284 -0.29994027 -0.33844678 -0.56141689 -0.60106166
[7,] -0.058940206 0.007642152 0.11279897 0.26618878 0.34021914 0.12044798
[8,] -0.013599882 -0.022894508 -0.05108028 -0.07337034 0.20591758 0.42187623
[9,] 0.058132664 -0.019947473 -0.23872658 -0.12873700 -0.08983879 -0.10481746
[10,] 0.097962458 -0.087049086 0.03092690 0.21333862 0.17388535 0.35881460
[11,] -0.005242558 -0.176666526 -0.31605647 -0.44823683 -0.52553149 -0.60865613
[12,] 0.169623092 0.454902738 0.34030739 0.25360809 0.48977920 0.70244208
[13,] -0.112301966 -0.098287927 -0.13187607 -0.32862396 -0.32293773 -0.38635237
[14,] -0.207170659 -0.452541018 -0.48725481 -0.54562355 -0.56877525 -0.48453277
[15,] -0.011585917 -0.070866627 -0.08601789 -0.11544685 -0.28550869 -0.40243054
[16,] 0.088355732 -0.001778250 -0.23793422 -0.23179180 -0.22724522 -0.32640984
[17,] -0.471432890 -0.166582914 -0.14858704 -0.17622514 -0.23330163 -0.18028786
[18,] 0.116170849 0.091494221 0.14581693 0.24232104 0.20769770 0.31082621
[19,] -0.038285914 0.175436827 0.16683474 0.43668378 0.47491775 0.52426188
[20,] 0.017430006 0.205527254 0.37050750 0.46425291 0.42370374 0.56890108
[21,] 0.108960420 0.419941594 0.54024114 0.48736753 0.54821862 0.54054893
[22,] -0.039596596 -0.077070324 -0.19065391 -0.27974143 -0.43788224 -0.59464966
[23,] 0.442744631 0.241431083 0.17041923 0.49265412 0.29098186 0.19119920
[24,] 0.221246834 0.005913494 -0.21853777 -0.33109664 -0.45278051 -0.49277290
[25,] -0.182912603 -0.141976000 -0.12946374 0.18310210 0.22885599 0.12683630
[,12] [,13] [,14] [,15] [,16] [,17]
[1,] -0.0627261876 -0.04808565 0.10140161 0.27981591 0.2876442 0.17728440
[2,] 0.0136128264 -0.04267433 -0.13429325 -0.31750023 -0.5132658 -0.40314165
[3,] -0.3611412485 -0.41957394 -0.46605520 -0.60550023 -0.5060128 -0.38323262
[4,] -0.1530030329 -0.28869582 -0.32498540 -0.22798818 -0.1235555 0.08017662
[5,] -0.7418415824 -0.77490234 -0.67857842 -0.59518807 -0.6169946 -0.45725606
[6,] -0.5839475846 -0.88061781 -0.94217365 -0.87524984 -0.7526885 -0.70334132
[7,] -0.0007043639 -0.02587016 -0.03632620 0.04150492 0.1451866 0.08221413
[8,] 0.4176404526 0.15187302 0.21176204 0.36038190 0.4164684 0.51806676
[9,] -0.1515925653 -0.21377979 -0.21375890 -0.19723862 -0.1934741 -0.39320548
[10,] 0.4587988997 0.39172603 0.38196971 0.38688552 0.3824060 0.16916669
[11,] -0.5554188169 -0.56845232 -0.49868948 -0.37643675 -0.6190908 -0.64264265
[12,] 0.9507755496 0.97620393 0.63984545 0.63413334 0.5139189 0.51735065
[13,] -0.5067805000 -0.38197291 -0.42483001 -0.63364366 -0.7676287 -0.79298666
[14,] -0.3667882354 -0.35314550 -0.40851304 -0.61020711 -0.5950271 -0.41910221
[15,] -0.2789807335 -0.23745379 -0.37763214 -0.62364415 -0.7361117 -0.83423594
[16,] -0.4371953042 -0.50455300 -0.53260148 -0.66772830 -0.5023135 -0.47163486
[17,] -0.1671639946 0.03413930 -0.20944238 -0.25005872 -0.2004442 -0.37285900
[18,] 0.1764911928 -0.01282572 0.09841788 0.18496773 0.3467053 0.37398897
[19,] 0.3563364810 0.38215305 0.39501338 0.45351289 0.4452960 0.31412553
[20,] 0.6073526994 0.50463572 0.35440716 0.17028795 0.2209404 0.40128008
[21,] 0.6381131553 0.81096398 0.94294903 1.04023626 1.0660009 0.87135460
[22,] -0.5564309310 -0.54747318 -0.54878540 -0.63066240 -0.5743314 -0.63898620
[23,] 0.5729444768 0.78520827 0.57315018 0.35673672 0.3304408 0.09231623
[24,] -0.6597836224 -0.70420155 -0.76429165 -0.81463512 -0.5869100 -0.50448512
[25,] 0.1040206054 0.12937736 0.09502333 0.34969369 0.5506657 0.43398075
[,18] [,19] [,20] [,21] [,22] [,23]
[1,] 0.3164840 0.1445400 0.10077901 0.00852180 -0.21953087 -0.29090694
[2,] -0.3399458 -0.6649248 -0.81128576 -0.72710662 -0.57221706 -0.71510023
[3,] -0.5824461 -0.6172923 -0.67263281 -0.80946894 -0.79931787 -0.84010073
[4,] 0.1616014 0.1373852 0.08279394 -0.01382096 0.01028605 0.08875136
[5,] -0.4991487 -0.6892571 -0.91640597 -0.86617178 -0.94810776 -0.94003933
[6,] -0.6290075 -0.6922668 -0.72541560 -0.86876823 -0.60835702 -0.37706761
[7,] 0.1022407 -0.1211464 -0.09223257 -0.08387760 -0.23501236 -0.23911223
[8,] 0.1638254 0.1940516 0.26019142 0.32061629 0.38011335 0.14240906
[9,] -0.4075238 -0.3465376 -0.39408959 -0.37811937 -0.41560414 -0.56925723
[10,] 0.1985239 0.3294662 0.28532068 0.24136442 0.21068745 0.07448571
[11,] -0.5046906 -0.4966236 -0.39686405 -0.31957520 -0.32441381 -0.18160903
[12,] 0.7232962 0.7650431 0.72095128 0.51996893 0.30531805 0.10589640
[13,] -0.9079439 -0.8170250 -0.71302051 -0.88704213 -0.79266140 -0.85035235
[14,] -0.2634753 -0.1747692 -0.27246972 -0.29622365 -0.22445702 -0.26897603
[15,] -0.8790281 -0.8557447 -0.75204448 -0.65495129 -0.64127847 -0.68645875
[16,] -0.5539394 -0.5110058 -0.35068354 -0.28663777 -0.28571945 -0.44913956
[17,] -0.5745536 -0.6344507 -0.60939975 -0.55781821 -0.56358481 -0.71503479
[18,] 0.3269919 0.3214668 0.41812058 0.39040630 0.30686581 0.35365230
[19,] 0.4727602 0.3730297 0.61647525 0.74350607 0.91419996 0.71803208
[20,] 0.3567726 0.1838821 0.16653931 0.35328856 0.33050684 0.29210929
[21,] 0.9193170 1.0241477 0.98729194 0.88608924 0.68040143 0.86949718
[22,] -0.7517906 -0.8480210 -0.88084587 -0.85299669 -0.67490671 -0.74678885
[23,] 0.3209476 0.2249833 0.02215452 0.17216314 0.30511300 0.29412994
[24,] -0.7212447 -0.9870594 -1.02194675 -0.98197183 -1.09016930 -1.10190669
[25,] 0.4005941 0.3948492 0.35226820 0.30721750 0.16528181 0.32697062
[,24] [,25] [,26] [,27] [,28] [,29]
[1,] -0.03097278 0.15649649 0.2577411 0.192280244 0.19479613 0.26338722
[2,] -0.77221407 -0.62154926 -0.6469566 -0.651166378 -0.53056833 -0.39504833
[3,] -0.56585073 -0.57091100 -0.6350262 -0.627464934 -0.79354598 -0.73303236
[4,] 0.21635939 0.22043850 0.1647388 0.149929621 0.13541434 0.05105501
[5,] -0.87777527 -0.84256169 -0.7072264 -0.660422499 -0.80435313 -0.70340828
[6,] -0.40257590 -0.51654890 -0.4409188 -0.535163829 -0.58221898 -0.53675311
[7,] -0.22236733 -0.19323112 -0.1445099 0.059131732 0.03271889 0.12060060
[8,] 0.05965163 0.13719850 0.1915885 0.154765324 0.25815843 0.37630075
[9,] -0.50837068 -0.62244170 -0.7232894 -0.710800637 -0.82606612 -0.97247413
[10,] 0.06583498 -0.03400734 -0.1737843 0.004037726 0.22242282 0.29156566
[11,] -0.23774535 -0.31961435 -0.4364410 -0.346537480 -0.40262756 -0.12807684
[12,] -0.26757402 -0.23277359 -0.2824603 -0.279099364 -0.18982342 -0.25434249
[13,] -0.79841814 -0.60434585 -0.4342547 -0.397716251 -0.44663863 -0.33309019
[14,] -0.44133866 -0.50503472 -0.5159527 -0.477857106 -0.40320487 -0.43264494
[15,] -0.55456512 -0.35615813 -0.3610274 -0.556195620 -0.68503473 -0.74348711
[16,] -0.49267895 -0.49316291 -0.5012537 -0.505570638 -0.36870343 -0.36897761
[17,] -0.72265629 -0.60102007 -0.6182628 -0.792531948 -0.67884721 -0.66438548
[18,] 0.48443097 0.54323839 0.5544753 0.362919176 0.41518983 0.28105380
[19,] 0.59550485 0.77686111 0.7632639 0.838201567 0.89937735 0.79889456
[20,] 0.25008177 0.24436260 0.2078207 0.140976200 0.30986859 0.26845084
[21,] 1.12049270 1.17476101 1.1110483 1.347116154 1.29658092 1.18750781
[22,] -1.02047660 -0.85323741 -0.7142255 -0.847776177 -0.78493221 -0.83697003
[23,] 0.30357227 0.20805550 0.3316708 0.528378395 0.57160130 0.73161880
[24,] -1.18620156 -1.42640108 -1.4925071 -1.417038333 -1.52764107 -1.47372874
[25,] 0.35289271 0.28603428 0.3281623 0.338388913 0.17779264 0.18119271
[,30] [,31] [,32] [,33] [,34] [,35]
[1,] 0.2696501 0.26246134 0.25804478 0.539746938 0.45002651 0.31202216
[2,] -0.4204324 -0.38169906 -0.59628563 -0.862804714 -0.89872575 -0.96322435
[3,] -0.7867841 -0.84289688 -0.79397504 -0.792933551 -0.74381403 -0.54253361
[4,] -0.1042733 -0.15952125 -0.31300513 -0.258292910 -0.34556970 -0.39245288
[5,] -0.7311721 -0.62448118 -0.66813754 -0.637712181 -0.81822770 -0.62296963
[6,] -0.5180713 -0.57103896 -0.51496671 -0.548721865 -0.44643962 -0.36029998
[7,] 0.1564898 0.19247577 0.23330202 0.230454531 0.18200720 0.29962276
[8,] 0.1541725 0.15036501 0.21371085 0.269343095 0.28703193 0.36097773
[9,] -1.0481211 -0.86203221 -0.89438269 -0.979310960 -1.08249992 -1.28857505
[10,] 0.4232740 0.38087024 0.35795705 0.597319216 0.83973078 0.98769992
[11,] -0.1464334 0.01453361 0.08177047 -0.002599172 0.10514956 0.17985268
[12,] -0.2381766 0.11204474 0.29309964 0.297137512 0.54917765 0.65450197
[13,] -0.2126470 -0.24583037 -0.17879972 -0.146785940 -0.24036789 -0.14103289
[14,] -0.6920330 -0.74769993 -0.84764534 -0.602224357 -0.62192803 -0.65552585
[15,] -0.5797694 -0.36469285 -0.13699601 -0.208951321 -0.34311121 -0.39443499
[16,] -0.4868647 -0.48982106 -0.44930916 -0.316235987 -0.27925463 -0.30428746
[17,] -0.8952332 -0.96523955 -0.87645136 -0.909004165 -0.85730041 -0.62653165
[18,] 0.1495326 0.26335209 0.25177504 0.131599002 0.26411379 0.35815192
[19,] 0.7990696 0.80656947 0.83833501 0.810458611 0.59694265 0.44376325
[20,] 0.1027327 0.02987103 0.04451289 -0.020347743 -0.03611004 0.07176579
[21,] 1.0792659 0.79986178 0.79118811 0.950072992 0.85367189 0.69054268
[22,] -0.6118399 -0.53035953 -0.70095680 -0.717188273 -0.63628481 -0.47623161
[23,] 0.9328934 0.75688362 0.74905435 0.728192057 0.75102039 0.47094196
[24,] -1.4303912 -1.43911142 -1.15824049 -1.299806175 -1.26234898 -1.36949326
[25,] 0.1692371 0.23224599 0.16164251 0.122231985 0.02984007 -0.04913621
[,36] [,37] [,38] [,39] [,40] [,41]
[1,] 0.227516176 0.35700207 0.4730786 0.44892673 0.46397019 0.5873787
[2,] -0.889875429 -0.88591260 -1.0269245 -0.81834435 -0.77437286 -0.9689864
[3,] -0.570784671 -0.56505917 -0.5928198 -0.51496148 -0.31381091 -0.1846533
[4,] -0.427691692 -0.47757734 -0.5532234 -0.44180332 -0.56750486 -0.7165488
[5,] -0.238889661 -0.25992181 -0.2296763 -0.30804256 -0.42307756 -0.4047407
[6,] -0.313834292 -0.39967991 -0.4650776 -0.33108613 -0.32280760 -0.1039933
[7,] 0.349850762 0.32781268 0.2834297 0.26132216 0.28064139 0.2809944
[8,] 0.474251378 0.41337075 0.3315951 0.38951147 0.24008764 0.3384315
[9,] -1.439341029 -1.25875445 -1.3123808 -1.35886701 -1.33798029 -1.0892190
[10,] 1.042079209 0.97416672 0.9651118 0.91518828 0.98042522 0.9012418
[11,] 0.178806023 0.06751553 -0.0563677 -0.27665847 -0.21171180 -0.1714802
[12,] 0.572464126 0.48148542 0.4441376 0.25607096 0.52428470 0.5672569
[13,] -0.295466889 -0.29567244 -0.1145172 -0.24332127 -0.22761490 -0.2095197
[14,] -0.638960400 -0.68851751 -0.7772524 -0.71528919 -0.56195470 -0.3600272
[15,] -0.415036668 -0.63657169 -0.6486015 -0.78002837 -0.79563379 -0.9355270
[16,] -0.210357292 -0.27019406 -0.5119269 -0.69127388 -0.55931470 -0.3762951
[17,] -0.533246818 -0.42302931 -0.2886576 -0.14340423 -0.09842852 -0.1121804
[18,] 0.285205146 0.24377733 0.2133235 0.09115598 0.24492667 0.1862679
[19,] 0.533847412 0.47593836 0.4533771 0.45742334 0.19160804 0.0370288
[20,] 0.004363698 0.07026225 0.1443233 0.32476805 0.20211291 0.2511295
[21,] 0.692723243 0.85393521 0.9336330 1.25892208 1.06251754 1.0916274
[22,] -0.730322314 -0.63219073 -0.5180803 -0.62198597 -0.51926105 -0.6035236
[23,] 0.369801859 0.32661169 0.3118453 0.30425889 0.37387976 0.3483269
[24,] -1.305593663 -1.49450791 -1.3194519 -1.09693957 -1.08932359 -1.1187674
[25,] 0.115217878 0.17033564 0.1863939 0.29312042 0.31855103 0.2947031
[,42] [,43] [,44] [,45] [,46]
[1,] 0.535466552 0.44659682 0.621293156 0.50376099 0.645602471
[2,] -1.020769117 -1.12375508 -1.154463873 -1.26336567 -1.253965134
[3,] -0.139771565 -0.20901211 -0.139619992 0.10912634 0.199085805
[4,] -0.700733269 -0.65084610 -0.710340210 -0.69347829 -0.661449716
[5,] -0.139375168 -0.15898862 -0.215713078 -0.01503931 0.161985347
[6,] 0.008161673 -0.03426967 -0.087930249 -0.12380376 -0.290408177
[7,] 0.213955450 0.18224529 0.065450878 -0.29458417 -0.248686928
[8,] 0.273635255 0.31031464 0.119613649 0.20544588 0.211446625
[9,] -0.996806114 -0.99947479 -0.781647767 -0.73955080 -0.742713952
[10,] 0.826978231 1.07736826 1.006897268 0.93598576 0.938633731
[11,] -0.101885526 -0.07293279 -0.004412092 -0.06062433 0.008344603
[12,] 0.435298149 0.61981361 0.770906844 0.86109577 0.864430264
[13,] -0.172640750 -0.31411075 -0.426822811 -0.34398528 -0.433454820
[14,] -0.426668897 -0.33243502 -0.204311843 -0.39657141 -0.197176302
[15,] -0.986866909 -0.89939402 -0.844164457 -0.90693616 -0.763826859
[16,] -0.387180844 -0.52166912 -0.510986444 -0.35416605 -0.408887837
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[18,] 0.253644759 0.18265546 0.328468855 0.27142929 0.168620632
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[20,] 0.275905772 0.22134600 0.220244542 0.40216250 0.553632357
[21,] 1.068828612 1.21931117 1.212515958 1.12155905 1.224400920
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[23,] 0.192731653 0.21279998 0.111164114 0.21144350 0.140033017
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[25,] 0.285705421 0.14322170 0.165865360 0.14622922 0.179868656
[,47] [,48] [,49] [,50]
[1,] 0.544424444 0.61747225 0.44370311 0.601970256
[2,] -1.389417066 -1.56050010 -1.63721864 -1.677892047
[3,] 0.221519910 0.15573717 0.06309499 0.087687147
[4,] -0.727798910 -0.73856861 -0.65838119 -0.589577218
[5,] 0.045546717 -0.02269264 -0.17673326 -0.150830508
[6,] -0.607643102 -1.00467901 -1.22380908 -0.918584745
[7,] -0.198982500 -0.17610410 -0.07511532 0.088568040
[8,] 0.236670621 0.27902485 0.14598850 -0.003333688
[9,] -1.079510855 -1.17265260 -1.33929292 -1.339854776
[10,] 0.855158852 0.78262975 0.76000683 0.696825336
[11,] 0.006504764 -0.04418811 0.14795288 0.202140302
[12,] 0.810443649 0.84366213 0.81137131 0.810732460
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[17,] -0.350007062 -0.42070011 -0.46093727 -0.186831193
[18,] 0.054543396 0.10036674 0.12636592 0.011695115
[19,] 0.261463562 0.16183895 0.21861505 0.438125770
[20,] 0.691709931 0.68655781 0.79461913 0.598228125
[21,] 1.428556563 1.60379618 1.48946181 1.572525477
[22,] -0.621139513 -0.67126409 -0.80063580 -0.676649162
[23,] -0.085318584 -0.09688383 0.14249458 0.187914185
[24,] -1.535564586 -1.54567673 -1.46811244 -1.372403062
[25,] 0.219492648 0.18673643 0.54327762 0.687353173
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