Publication Information

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1030, 1074, 1104], 'the': [18, 46, 52, 63, 140, 186, 214, 240, 243, 348, 385, 392, 458, 473, 489, 538, 573, 579, 677, 683, 698, 723, 755, 793, 799, 826, 851, 862, 872, 921, 1031, 1043, 1053, 1059, 1075, 1079, 1092, 1102, 1105], 'Distribution': [19, 143, 828, 853, 864, 995], 'Function.-': [20, 144, 154, 529, 854, 865], '1.2': [21], 'Fokker-Planck': [22, 25, 31, 40, 47, 53, 64, 221, 252, 280, 302, 349, 352, 393, 447, 474, 490, 802, 943, 1044, 1060, 1080, 1095, 1151, 1159], '1.2.1': [24], 'One': [28, 164, 255, 355, 1093], 'Variable.-': [29, 165, 256, 313, 575], '1.2.2': [30], 'N': [34, 283], 'Variables.-': [35, 91, 105, 121, 182, 197, 284, 306, 343, 495, 541, 554, 560, 566, 689, 822], '1.2.3': [36], 'How': [37, 199], 'Does': [38], 'a': [39, 319, 429, 435, 461, 467, 708, 784, 959, 980, 1026, 1125, 1154], 'Arise?.-': [42], '1.2.4': [43], 'Purpose': [44], '1.2.5': [49], 'Solutions': [50, 212, 241, 459, 584, 613, 629, 675, 706, 721, 844, 883, 887, 1057, 1090], '1.2.6': [55], 'Kramers': [56, 678, 684, 724], 'and': [57, 78, 84, 174, 191, 203, 245, 270, 405, 412, 418, 443, 523, 548, 592, 598, 643, 692, 716, 744, 750, 801, 820, 840, 879, 914, 918, 948, 1019, 1088, 1111, 1130, 1158], 'Smoluchowski': [58], 'Equations.-': [59, 124, 247, 595, 655, 659, 803, 933], '1.2.7': [60], 'Generalizations': [61], '1.3': [66], 'Boltzmann': [67, 1015], '1.4': [69], 'Master': [70], '2.': [72], 'Probability': [73, 79, 94, 259, 286, 290, 294, 903], 'Theory.-': [74], '2.1': [75], 'Random': [76, 90, 104, 120], 'Variable': [77, 356, 1094], 'Density.-': [80, 95], '2.2': [81], 'Characteristic': [82], 'Function': [83, 757], 'Cumulants.-': [85], '2.3': [86], 'Generalization': [87], 'to': [88, 200, 460, 501, 572, 578, 590, 792, 818, 1052, 1086], 'Several': [89, 118, 181, 305, 450], '2.3.1': [92], 'Conditional': [93], '2.3.2': [96], 'Cross': [97], 'Correlation.-': [98], '2.3.3': [99], 'Gaussian': [100, 1012], 'Distribution.-': [101, 291, 992], '2.4': [102], 'Time-Dependent': [103, 119, 650, 811], '2.4.1': [106], 'Classification': [107], 'Processes.-': [110, 272], '2.4.2': [111], 'Chapman-Kolmogorov': [112], '2.4.3': [114], 'Wiener-Khintchine': [115], 'Theorem.-': [116, 250], '2.5': [117], '3.': [122], 'Langevin': [123, 126, 162, 179, 187, 215, 800, 939], '3.1': [125], '3.1.1': [131], 'Mean-Squared': [132], 'Displacement.-': [133], '3.1.2': [134], 'Three-Dimensional': [135, 308, 322], 'Case.-': [136], '3.1.3': [137], 'Calculation': [138, 149, 860, 1139], 'Stationary': [141, 363, 619, 808, 827, 843, 852, 863, 946], 'Velocity': [142], '3.2': [145], 'Ornstein-Uhlenbeck': [146, 366, 482], 'Process.-': [147, 367, 483], '3.2.1': [148], 'Moments.-': [151], '3.2.2': [152], 'Correlation': [153, 524, 531, 1141], '3.2.3': [155], 'Solution': [156, 947, 962, 984], 'by': [157, 217, 963, 1062], 'Fourier': [158], 'Transformation.-': [159], '3.3': [160], 'Nonlinear': [161, 178], 'Equation,': [163], '3.3.1': [166], 'Example.-': [167], '3.3.2': [168], 'Kramers-Moyal': [169, 224, 231, 277, 1068], 'Expansion': [170, 427, 465, 509, 701, 740, 753, 953, 957, 978, 1069, 1108], 'Coefficients.-': [171, 193], '3.3.3': [172], "Ito's": [173], "Stratonovich's": [175], 'Definitions.-': [176], '3.4': [177], 'Equations,': [180], '3.4.1': [183], 'Determination': [184, 747, 968], 'from': [189], 'Drift': [190, 202, 547], 'Diffusion': [192, 204, 433, 549, 899, 1156], '3.4.2': [194], 'Transformation': [195, 341, 471, 493, 696, 817], '3.4.3': [198], 'Obtain': [201], 'Coefficients': [205, 550], 'Systems.-': [207], '3.5': [208], 'Markov': [209], 'Property.-': [210], '3.6': [211], 'Computer': [218, 1063], 'Simulation.-': [219], '4.': [220], '4.1': [223], 'Forward': [225, 244], 'Expansion.-': [226, 233, 370, 736], '4.1.1': [227], 'Formal': [228, 235], 'Solution.-': [229, 236, 359, 364, 454, 463, 620, 809, 812, 881, 973], '4.2': [230], 'Backward': [232, 246], '4.2.1': [234], '4.2.2': [237], 'Equivalence': [238], '4.3': [248], 'Pawula': [249], '4.4': [251], '4.4.1': [257], 'Transition': [258, 293, 712, 902], 'Density': [260, 295], 'Small': [262, 297], 'Times.-': [263, 298, 906], '4.4.2': [264], 'Path': [265], 'Integral': [266], 'Solutions.-': [267, 897], '4.5': [268], 'Generation': [269], 'Recombination': [271], '4.6': [273], 'Application': [274, 589], 'Truncated': [276], 'Expansions.-': [278, 477], '4.7': [279], '4.7.1': [285], 'Current.-': [287], '4.7.2': [288], 'Joint': [289], '4.7.3': [292], '4.8': [299], 'Examples': [300], 'Equations': [303, 646, 935, 1009], 'with': [304, 570, 647, 1010, 1017, 1153, 1161], '4.8.1': [307], 'without': [311], 'Position': [312], '4.8.2': [314], 'One-Dimensional': [315], 'in': [318, 325, 336, 765, 783, 920, 954, 1124], 'Potential.-': [320, 339, 375, 379, 387, 402, 445, 874], '4.8.3': [321], 'an': [326, 337, 502], 'External': [327, 338], 'Force.-': [328, 710], '4.8.4': [329], 'Two': [333], 'Interacting': [334], 'Particles': [335], '4.9': [340], '4.10': [344], 'Covariant': [345, 1076], 'Form': [346, 1077], '5.': [351], 'Methods': [357, 414, 452, 486, 661], '5.1': [360], 'Normalization.-': [361], '5.2': [362], '5.3': [365], '5.4': [368], 'Eigenfunction': [369, 476, 975], '5.5': [371], 'Examples.-': [372], '5.5.1': [373], 'Parabolic': [374, 378], '5.5.2': [376], 'Inverted': [377, 408], '5.5.3': [380], 'Infinite': [381], 'Square': [382], 'Well': [383], 'Schrudinger': [386], '5.5.4': [388], 'V-Shaped': [389], 'Potential': [390, 1103, 1127], '5.6': [395], 'Jump': [396], 'Conditions.-': [397], '5.7': [398], 'A': [399], 'Bistable': [400, 442], 'Model': [401], '5.8': [403], 'Eigenfunctions': [404, 919], 'Eigenvalues': [406, 417, 715, 749, 913, 917], 'Potentials.-': [409, 767], '5.9': [410], 'Approximate': [411], 'Numerical': [413, 424, 506], 'Determining': [416], 'Eigenfunctions.-': [419, 717, 915], '5.9.1': [420], 'Variational': [421, 497], 'Method.-': [422, 498, 516, 519, 858, 976], '5.9.2': [423], 'Integration.-': [425, 507], '5.9.3': [426], 'into': [428, 466, 510, 702, 958, 979], 'Complete': [430, 511, 960, 981], 'Set.-': [431, 469, 982], '5.10': [432], 'Over': [434], 'Barrier.-': [436], '5.10.1': [437], "Kramers'": [438], 'Escape': [439], 'Rate.-': [440], '5.10.2': [441], 'Metastable': [444], '6.': [446], 'Variables': [451], '6.1': [455], 'Approach': [456], 'Limit': [462], '6.2': [464], 'Biorthogonal': [468], '6.3': [470], 'Operator,': [475], '6.4': [478], 'Detailed': [479], 'Balance.-': [480], '6.5': [481], '6.6': [484, 1110], 'Further': [485, 1114], 'Solving': [488], '6.6.1': [492], '6.6.2': [496], '6.6.3': [499], 'Reduction': [500, 536], 'Hermitian': [503], 'Problem.-': [504, 624, 627, 637, 640, 729, 732], '6.6.4': [505], '6.6.5': [508], 'Sets.-': [512], '6.6.6': [513], 'Matrix': [514, 671, 719, 856, 868, 964, 1027, 1117, 1157], 'Continued-Fraction': [515, 720, 857], '6.6.7': [517], 'WKB': [518], '7.': [520], 'Linear': [521, 527, 568, 709], 'Response': [522, 528], 'Functions.-': [525, 532, 704, 829, 832, 835], '7.1': [526], '7.2': [530], '7.3': [533], 'Susceptibility.-': [534], '8.': [535], 'Number': [539], 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'Double-Well': [1126], '(Chaps.': [1128], '10': [1129], '11).-': [1131], 'S.8': [1132], 'Boundary': [1133], 'Layer': [1134], 'Theory': [1135], '11.4).-': [1137], 'S.9': [1138], 'Times': [1142], '7.12).-': [1144], 'S.10': [1145], '(Appendix': [1148], 'A1).-': [1149], 'S.11': [1150], 'Non-Positive-Definite': [1155], 'Additional': [1162], 'Third-Order-Derivative': [1163], 'Terms.-': [1164], 'References.': [1165]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2017277760', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 8}, {'year': 2022, 'cited_by_count': 18}, {'year': 2021, 'cited_by_count': 106}, {'year': 2020, 'cited_by_count': 118}, {'year': 2019, 'cited_by_count': 106}, {'year': 2018, 'cited_by_count': 75}, {'year': 2017, 'cited_by_count': 100}, {'year': 2016, 'cited_by_count': 97}, {'year': 2015, 'cited_by_count': 141}, {'year': 2014, 'cited_by_count': 153}, {'year': 2013, 'cited_by_count': 156}, {'year': 2012, 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