wiener.process: Create a Wiener Process

Description Usage Arguments Value Examples

View source: R/processes.R

Description

Create a Wiener Process

Usage

1
wiener.process(dispersion = 1)

Arguments

dispersion

the dispersion parameter of the Wiener process.

Value

a function hanlde in the form of X(tObs,n) which generates n independent trajectories observed at tObs.

Examples

1
2
X <- wiener.process()
X(regular.grid(50),25)

Example output

              [,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
[17,] -0.162468202  0.12242893  0.088894611 -0.19177172 -0.287483184
[18,]  0.253644759  0.18265546  0.328468855  0.27142929  0.168620632
[19,]  0.144518693 -0.03356825  0.037005398  0.02234700  0.280091942
[20,]  0.275905772  0.22134600  0.220244542  0.40216250  0.553632357
[21,]  1.068828612  1.21931117  1.212515958  1.12155905  1.224400920
[22,] -0.621356991 -0.42809795 -0.445486241 -0.50623036 -0.503434273
[23,]  0.192731653  0.21279998  0.111164114  0.21144350  0.140033017
[24,] -1.257293848 -1.36301936 -1.437775663 -1.54756822 -1.580920623
[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
[13,] -0.672128062 -0.62697374 -0.59406528 -0.392297884
[14,] -0.389946252 -0.37595059 -0.25858330 -0.057151092
[15,] -0.877381082 -0.81980502 -0.70863683 -0.683307750
[16,] -0.610965055 -0.62727228 -0.54002344 -0.479521486
[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

synfd documentation built on July 1, 2020, 6:04 p.m.