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Volumn 19, Issue , 2014, Pages 1-24

Causal interpretation of stochastic differential equations

Author keywords

Causality; Identifiability; L vy process; Stochastic differential equation; Structural equation model; Weak conditional local independence

Indexed keywords


EID: 84908285303     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v19-2891     Document Type: Article
Times cited : (47)

References (38)
  • 2
    • 84861505778 scopus 로고    scopus 로고
    • Continuous time Markov chain models for chemical reaction networks
    • Springer, Heidelberg
    • D. Anderson and T. G. Kurtz, Continuous time Markov chain models for chemical reaction networks, Design and Analysis of Biomolecular Circuits, Springer, Heidelberg, 2011, pp. 3- 42.
    • (2011) Design and Analysis of Biomolecular Circuits , pp. 3-42
    • Anderson, D.1    Kurtz, T.G.2
  • 3
    • 77953146446 scopus 로고    scopus 로고
    • Lévy processes and stochastic calculus
    • second ed., Cambridge University Press, Cambridge, MR-2512800
    • D. Applebaum, Lévy processes and stochastic calculus, second ed., Cambridge Studies in Advanced Mathematics, vol. 116, Cambridge University Press, Cambridge, 2009. MR-2512800
    • (2009) Cambridge Studies in Advanced Mathematics , vol.116
    • Applebaum, D.1
  • 5
    • 66849097832 scopus 로고    scopus 로고
    • A general dynamical statistical model with causal interpretation
    • MR-2749916
    • D. Commenges and A. Gégout-Petit, A general dynamical statistical model with causal interpretation, J. R. Stat. Soc. Ser. B Stat. Methodol. 71 (2009), no. 3, 719-736. MR-2749916
    • (2009) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.71 , Issue.3 , pp. 719-736
    • Commenges, D.1    Gégout-Petit, A.2
  • 6
    • 0030532763 scopus 로고    scopus 로고
    • Noncausality in continuous time models
    • MR-1395031
    • F. Comte and E. Renault, Noncausality in continuous time models, Econometric Theory 12 (1996), no. 2, 215-256. MR-1395031
    • (1996) Econometric Theory , vol.12 , Issue.2 , pp. 215-256
    • Comte, F.1    Renault, E.2
  • 7
    • 1542742382 scopus 로고    scopus 로고
    • Causal inference without counterfactuals
    • With comments and a rejoinder by the author. MR-1803167
    • A. P. Dawid, Causal inference without counterfactuals, J. Amer. Statist. Assoc. 95 (2000), no. 450, 407-448, With comments and a rejoinder by the author. MR-1803167
    • (2000) J. Amer. Statist. Assoc. , vol.95 , Issue.450 , pp. 407-448
    • Dawid, A.P.1
  • 8
    • 37849044185 scopus 로고    scopus 로고
    • Graphical models for marked point processes based on local independence
    • MR-2412641
    • V. Didelez, Graphical models for marked point processes based on local independence, J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008), no. 1, 245-264. MR-2412641
    • (2008) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.70 , Issue.1 , pp. 245-264
    • Didelez, V.1
  • 9
    • 33847242530 scopus 로고    scopus 로고
    • Granger causality and path diagrams for multivariate time series
    • MR-2354948
    • M. Eichler, Granger causality and path diagrams for multivariate time series, J. Econometrics 137 (2007), no. 2, 334-353. MR-2354948
    • (2007) J. Econometrics , vol.137 , Issue.2 , pp. 334-353
    • Eichler, M.1
  • 10
    • 84861778291 scopus 로고    scopus 로고
    • Graphical modelling of multivariate time series
    • MR-2925574
    • M. Eichler, Graphical modelling of multivariate time series, Probab. Theory Related Fields 153 (2012), no. 1-2, 233-268. MR-2925574
    • (2012) Probab. Theory Related Fields , vol.153 , Issue.1-2 , pp. 233-268
    • Eichler, M.1
  • 11
    • 77950462635 scopus 로고    scopus 로고
    • On Granger causality and the effect of interventions in time series
    • MR-2575937
    • M. Eichler and V. Didelez, On Granger causality and the effect of interventions in time series, Lifetime Data Anal. 16 (2010), no. 1, 3-32. MR-2575937
    • (2010) Lifetime Data Anal. , vol.16 , Issue.1 , pp. 3-32
    • Eichler, M.1    Didelez, V.2
  • 12
    • 10244239321 scopus 로고    scopus 로고
    • Life with 6000 genes
    • A. Gofieau et al., Life with 6000 genes, Science 274 (1996), no. 5287, 546-567.
    • (1996) Science , vol.274 , Issue.5287 , pp. 546-567
    • Gofieau, A.1
  • 13
    • 0034616930 scopus 로고    scopus 로고
    • Functional discovery via a compendium of expression profiles
    • T. R. Hughes et al., Functional discovery via a compendium of expression profiles, Cell 102 (2000), 109-126.
    • (2000) Cell , vol.102 , pp. 109-126
    • Hughes, T.R.1
  • 15
    • 0030369935 scopus 로고    scopus 로고
    • Noncausality in continuous time
    • MR-1403234
    • J.-P. Florens and D. Fougere, Noncausality in continuous time, Econometrica 64 (1996), no. 5, 1195-1212. MR-1403234
    • (1996) Econometrica , vol.64 , Issue.5 , pp. 1195-1212
    • Florens, J.-P.1    Fougere, D.2
  • 16
    • 77950465761 scopus 로고    scopus 로고
    • A general definition of influence between stochastic processes
    • MR-2575938
    • A. Gégout-Petit and D. Commenges, A general definition of influence between stochastic processes, Lifetime Data Anal. 16 (2010), no. 1, 33-44. MR-2575938
    • (2010) Lifetime Data Anal. , vol.16 , Issue.1 , pp. 33-44
    • Gégout-Petit, A.1    Commenges, D.2
  • 17
    • 0023592965 scopus 로고
    • Causality and stochastic dynamic systems
    • MR-0916245
    • J. B. Gill and L. Petrović, Causality and stochastic dynamic systems, SIAM J. Appl. Math. 47 (1987), no. 6, 1361-1366. MR-0916245
    • (1987) SIAM J. Appl. Math. , vol.47 , Issue.6 , pp. 1361-1366
    • Gill, J.B.1    Petrović, L.2
  • 18
    • 67650872475 scopus 로고    scopus 로고
    • Distributions and operators
    • Springer, New York, MR-2453959
    • G. Grubb, Distributions and operators, Graduate Texts in Mathematics, vol. 252, Springer, New York, 2009. MR-2453959
    • (2009) Graduate Texts in Mathematics , vol.252
    • Grubb, G.1
  • 20
    • 0009158870 scopus 로고
    • A brief account of the theory of homogeneous Gaussian diffusions in finite dimensions
    • TVP Science Publishers
    • M. Jacobsen, A brief account of the theory of homogeneous Gaussian diffusions in finite dimensions, Frontiers in Pure and Applied Probability 1, TVP Science Publishers, 1993, pp. 86-94.
    • (1993) Frontiers in Pure and Applied Probability 1 , pp. 86-94
    • Jacobsen, M.1
  • 22
    • 77951641247 scopus 로고    scopus 로고
    • Predicting causal effects in large-scale systems from observational data
    • M. H. Maathuis, D. Colombo, M. Kalisch, and P. Bühlmann, Predicting causal effects in large-scale systems from observational data, Nature Methods (2010), no. 4, 247-248.
    • (2010) Nature Methods , Issue.4 , pp. 247-248
    • Maathuis, M.H.1    Colombo, D.2    Kalisch, M.3    Bühlmann, P.4
  • 23
    • 69949166983 scopus 로고    scopus 로고
    • Estimating high-dimensional intervention effects from observational data
    • MR-2549555
    • M. H. Maathuis, M. Kalisch, and P. Bühlmann, Estimating high-dimensional intervention effects from observational data, Ann. Statist. 37 (2009), no. 6A, 3133-3164. MR-2549555
    • (2009) Ann. Statist. , vol.37 , Issue.6 A , pp. 3133-3164
    • Maathuis, M.H.1    Kalisch, M.2    Bühlmann, P.3
  • 24
    • 0000314740 scopus 로고
    • Lifetime portfolio selection under uncertainty: The continuous-time case
    • R. C. Merton, Lifetime portfolio selection under uncertainty: the continuous-time case, Rev. Econ. Stat. 51 (1969), no. 3, 247-257.
    • (1969) Rev. Econ. Stat. , vol.51 , Issue.3 , pp. 247-257
    • Merton, R.C.1
  • 26
    • 70349349170 scopus 로고    scopus 로고
    • second ed., Cambridge University Press, Cambridge, Models, reasoning, and inference. MR-2548166
    • J. Pearl, Causality, second ed., Cambridge University Press, Cambridge, 2009, Models, reasoning, and inference. MR-2548166
    • (2009) Causality
    • Pearl, J.1
  • 27
    • 84908277840 scopus 로고    scopus 로고
    • Identifiability of Gaussian structural equation models with same error variances
    • to appear MR-3180667
    • J. Peters and P. Bühlmann, Identifiability of Gaussian structural equation models with same error variances, Biometrika, to appear (2014), 1-11. MR-3180667
    • (2014) Biometrika , pp. 1-11
    • Peters, J.1    Bühlmann, P.2
  • 28
    • 79957518899 scopus 로고    scopus 로고
    • Invariance of statistical causality under convergence
    • MR-2811860
    • L. Petrović and S. Dimitrijević, Invariance of statistical causality under convergence, Statist. Probab. Lett. 81 (2011), no. 9, 1445-1448. MR-2811860
    • (2011) Statist. Probab. Lett. , vol.81 , Issue.9 , pp. 1445-1448
    • Petrović, L.1    Dimitrijević, S.2
  • 29
    • 76649098294 scopus 로고    scopus 로고
    • Statistical causality, extremal measures and weak solutions of stochastic differential equations with driving semimartingales
    • MR-2596243
    • L. Petrović and D. Stanojević, Statistical causality, extremal measures and weak solutions of stochastic differential equations with driving semimartingales, J. Math. Model. Algorithms 9 (2010), no. 1, 113-128. MR-2596243
    • (2010) J. Math. Model. Algorithms , vol.9 , Issue.1 , pp. 113-128
    • Petrović, L.1    Stanojević, D.2
  • 30
    • 32844470231 scopus 로고    scopus 로고
    • Stochastic integration and differential equations
    • Springer-Verlag, Berlin, Second edition. Version 2.1, Corrected third printing. MR-2273672
    • P. E. Protter, Stochastic integration and differential equations, Stochastic Modelling and Applied Probability, vol. 21, Springer-Verlag, Berlin, 2005, Second edition. Version 2.1, Corrected third printing. MR-2273672
    • (2005) Stochastic Modelling and Applied Probability , vol.21
    • Protter, P.E.1
  • 32
    • 79960249370 scopus 로고    scopus 로고
    • A martingale approach to continuous-time marginal structural models
    • MR-2817610
    • K. Røysland, A martingale approach to continuous-time marginal structural models, Bernoulli 17 (2011), no. 3, 895-915. MR-2817610
    • (2011) Bernoulli , vol.17 , Issue.3 , pp. 895-915
    • Røysland, K.1
  • 33
    • 84908280913 scopus 로고    scopus 로고
    • Counterfactual analyses with graphical models based on local independence
    • MR-3059080
    • K. Røysland, Counterfactual analyses with graphical models based on local independence, Ann. Statist. 40 (2012), no. 4, 2162-2194. MR-3059080
    • (2012) Ann. Statist. , vol.40 , Issue.4 , pp. 2162-2194
    • Røysland, K.1
  • 34
    • 0003232762 scopus 로고    scopus 로고
    • Lévy processes and infinitely divisible distributions
    • Cambridge University Press, Cambridge, Translated from the 1990 Japanese original, Revised by the author. MR-1739520
    • K.-I. Sato, Lévy processes and infinitely divisible distributions, Cambridge Studies in Advanced Mathematics, vol. 68, Cambridge University Press, Cambridge, 1999, Translated from the 1990 Japanese original, Revised by the author. MR-1739520
    • (1999) Cambridge Studies in Advanced Mathematics , vol.68
    • Sato, K.-I.1
  • 35
    • 0007289040 scopus 로고    scopus 로고
    • Causation, prediction, and search
    • second ed., MIT Press, Cambridge, MA, With additional material by David Heckerman, Christopher Meek, Gregory F. Cooper and Thomas Richardson, A Bradford Book. MR-1815675
    • P. Spirtes, C. Glymour, and R. Scheines, Causation, prediction, and search, second ed., Adaptive Computation and Machine Learning, MIT Press, Cambridge, MA, 2000, With additional material by David Heckerman, Christopher Meek, Gregory F. Cooper and Thomas Richardson, A Bradford Book. MR-1815675
    • (2000) Adaptive Computation and Machine Learning
    • Spirtes, P.1    Glymour, C.2    Scheines, R.3
  • 37
    • 33750294583 scopus 로고    scopus 로고
    • Chapman & Hall/CRC Mathematical and Computational Biology Series, Chapman & Hall/CRC, Boca Raton, FL, MR-2222876
    • D. J. Wilkinson, Stochastic modelling for systems biology, Chapman & Hall/CRC Mathematical and Computational Biology Series, Chapman & Hall/CRC, Boca Raton, FL, 2006. MR-2222876
    • (2006) Stochastic Modelling for Systems Biology
    • Wilkinson, D.J.1


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