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Stochastics Volume 24, 1988 - Issue 4
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Original Articles

Reciprocal diffusions and stochastic differential equations of second orderFootnote∗

Arthur J. Krener Depattment of Mathematics and Institute of Theoretical Dynamics, University of California, Davis, CA, 95616, USA
Pages 393-422 | Received 27 Oct 1987, Published online: 04 Apr 2007

Citations (37)

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Read on this site (4)

Francesco Carravetta. (2008) Nearest-neighbour modelling of reciprocal chains. Stochastics 80:6, pages 525-584.
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Jerome M. Coleman, Bernard C. Levy & Arthur J. Krener. (1995) Gaussian reciprocal diffusions and positive definite sturm-liouville operators. Stochastics and Stochastic Reports 55:3-4, pages 279-313.
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Jerry Coleman. (1994) Gaussian reciprocal diffusions and their associated conservation laws. Stochastics and Stochastic Reports 51:3-4, pages 301-314.
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Arthur J. Krener, Ruggero Frezza & Bernard C. Levy. (1991) Gaussian reciprocal processes and self-adjoint stochastic differential equations of second order. Stochastics and Stochastic Reports 34:1-2, pages 29-56.
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Articles from other publishers (33)

Toshio MikamiToshio Mikami. 2021. Stochastic Optimal Transportation. Stochastic Optimal Transportation 1 19 .
Giovanni Conforti. (2018) A second order equation for Schrödinger bridges with applications to the hot gas experiment and entropic transportation cost. Probability Theory and Related Fields 174:1-2, pages 1-47.
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Reza Rezaie & X. Rong Li. (2018) Destination-Directed Trajectory Modeling and Prediction Using Conditionally Markov Sequences. Destination-Directed Trajectory Modeling and Prediction Using Conditionally Markov Sequences.
Reza Rezaie & X. Rong Li. (2018) Nonsingular Gaussian Conditionally Markov Sequences. Nonsingular Gaussian Conditionally Markov Sequences.
Giovanni Conforti & Max Von Renesse. (2017) Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges. Probability Theory and Related Fields 172:1-2, pages 493-524.
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Reza Rezaie & X. Rong Li. (2018) Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences. Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences.
Reza Rezaie & X. Rong Li. (2018) Gaussian Reciprocal Sequences from the Viewpoint of Conditionally Markov Sequences. Gaussian Reciprocal Sequences from the Viewpoint of Conditionally Markov Sequences.
Giovanni Conforti. (2018) Fluctuations of bridges, reciprocal characteristics and concentration of measure. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54:3.
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Giovanni Conforti & Christian Léonard. (2017) Reciprocal classes of random walks on graphs. Stochastic Processes and their Applications 127:6, pages 1870-1896.
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Giovanni Conforti, Paolo Dai Pra & Sylvie Rœlly. (2015) Reciprocal Class of Jump Processes. Journal of Theoretical Probability 30:2, pages 551-580.
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Yongxin Chen, Tryphon T. Georgiou & Michele Pavon. (2017) Optimal Transport Over a Linear Dynamical System. IEEE Transactions on Automatic Control 62:5, pages 2137-2152.
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Francesca Paola Carli. (2016) On the geometry of message passing algorithms for Gaussian reciprocal processes. On the geometry of message passing algorithms for Gaussian reciprocal processes.
Christian Léonard, Sylvie Rœlly & Jean-Claude Zambrini. (2014) Reciprocal processes. A measure-theoretical point of view. Probability Surveys 11:none.
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Sylvie Rœlly. 2014. Modern Stochastics and Applications. Modern Stochastics and Applications 53 67 .
Arthur J Krener. (2012) Filtering boundary value continuous time invariant linear systems. Filtering boundary value continuous time invariant linear systems.
Francesco Carravetta & Langford B. White. (2012) Modelling and Estimation for Finite State Reciprocal Processes. IEEE Transactions on Automatic Control 57:9, pages 2190-2202.
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Francesco Carravetta & Langford B. White. (2011) Two dimensional recursive optimal smoothing of Gaussian random fields. Two dimensional recursive optimal smoothing of Gaussian random fields.
Langford B White & Francesco Carravetta. (2011) Optimal Smoothing for Finite State Hidden Reciprocal Processes. IEEE Transactions on Automatic Control 56:9, pages 2156-2161.
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Francesco Carravetta. (2011) 2-D-Recursive Modelling of Homogeneous Discrete Gaussian Markov Fields. IEEE Transactions on Automatic Control 56:5, pages 1198-1203.
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Francesco Carravetta. (2009) 2D-recursive stochastic realization of discrete Gaussian Markov fields: the homogeneous case on a spheric domain. 2D-recursive stochastic realization of discrete Gaussian Markov fields: the homogeneous case on a spheric domain.
Francesco Carravetta. (2006) Representation of Non-Gaussian, Finite-States, Reciprocal Processes: the 1-D Problem with Cyclic Boundary Conditions. Representation of Non-Gaussian, Finite-States, Reciprocal Processes: the 1-D Problem with Cyclic Boundary Conditions.
Sylvie Roelly & Michèle Thieullen. (2005) Duality formula for the bridges of a Brownian diffusion: Application to gradient drifts. Stochastic Processes and their Applications 115:10, pages 1677-1700.
Crossref
Bernard C. Levy & Augusto Ferrante. (2002) Characterization of Stationary Discrete-Time Gaussian Reciprocal Processes over a Finite Interval. SIAM Journal on Matrix Analysis and Applications 24:2, pages 334-355.
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Bernard C Levy. (1997) Characterization of Multivariate Stationary Gaussian Reciprocal Diffusions. Journal of Multivariate Analysis 62:1, pages 74-99.
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J.M.F. Moura & S. Goswami. (1997) Gauss-Markov random fields (CMrf) with continuous indices. IEEE Transactions on Information Theory 43:5, pages 1560-1573.
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Bernard C. Levy & Arthur J. Krener. (1996) Stochastic mechanics of reciprocal diffusions. Journal of Mathematical Physics 37:2, pages 769-802.
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B. Delyon. (1995) Remarks on linear and nonlinear filtering. IEEE Transactions on Information Theory 41:1, pages 317-322.
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Bernard C. Levy & Arthur J. Krener. (1993) Dynamics and kinematics of reciprocal diffusions. Journal of Mathematical Physics 34:5, pages 1846-1875.
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M. Thieullen. (1993) Second order stochastic differential equations and non-Gaussian reciprocal diffusions. Probability Theory and Related Fields 97:1-2, pages 231-257.
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Paolo Dai Pra. (1991) A stochastic control approach to reciprocal diffusion processes. Applied Mathematics and Optimization 23:1, pages 313-329.
Crossref
B.C. Levy, R. Frezza & A.J. Krener. (1990) Modeling and estimation of discrete-time Gaussian reciprocal processes. IEEE Transactions on Automatic Control 35:9, pages 1013-1023.
Crossref
Paolo Dai Pra & Michele Pavon. 1990. Realization and Modelling in System Theory. Realization and Modelling in System Theory 497 504 .
Bernard C. Levy. 1990. Realization and Modelling in System Theory. Realization and Modelling in System Theory 13 21 .

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