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@ARTICLE{RydinGorjo:873131,
      author       = {Rydin Gorjão, Leonardo and Heysel, Jan and Lehnertz, Klaus
                      and Tabar, M. Reza Rahimi},
      title        = {{A}nalysis and data-driven reconstruction of bivariate
                      jump-diffusion processes},
      journal      = {Physical review / E},
      volume       = {100},
      number       = {6},
      issn         = {2470-0045},
      address      = {Woodbury, NY},
      publisher    = {APS},
      reportid     = {FZJ-2020-00576},
      pages        = {062127},
      year         = {2019},
      abstract     = {We introduce the bivariate jump-diffusion process,
                      consisting of two-dimensional diffusion and two-dimensional
                      jumps, that can be coupled to one another. We present a
                      data-driven, nonparametric estimation procedure of
                      higher-order (up to 8) Kramers-Moyal coefficients that
                      allows one to reconstruct relevant aspects of the underlying
                      jump-diffusion processes and to recover the underlying
                      parameters. The procedure is validated with numerically
                      integrated data using synthetic bivariate time series from
                      continuous and discontinuous processes. We further evaluate
                      the possibility of estimating the parameters of the
                      jump-diffusion model via data-driven analyses of the
                      higher-order Kramers-Moyal coefficients, and the limitations
                      arising from the scarcity of points in the data or
                      disproportionate parameters in the system.},
      cin          = {IEK-STE},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IEK-STE-20101013},
      pnm          = {153 - Assessment of Energy Systems – Addressing Issues of
                      Energy Efficiency and Energy Security (POF3-153) / ES2050 -
                      Energie Sytem 2050 (ES2050) / VH-NG-1025 - Helmholtz Young
                      Investigators Group "Efficiency, Emergence and Economics of
                      future supply networks" $(VH-NG-1025_20112014)$},
      pid          = {G:(DE-HGF)POF3-153 / G:(DE-HGF)ES2050 /
                      $G:(HGF)VH-NG-1025_20112014$},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:31962437},
      UT           = {WOS:000503814600003},
      doi          = {10.1103/PhysRevE.100.062127},
      url          = {https://juser.fz-juelich.de/record/873131},
}