1994
DOI: 10.1016/0375-9601(94)90150-3
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Conserved quantities and symmetry for stochastic dynamical systems

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Cited by 36 publications
(44 citation statements)
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“…, r) are Brownian motions. The first approach [3][4][5][6] deals with fiber-preserving transformations…”
Section: Introductionmentioning
confidence: 99%
“…, r) are Brownian motions. The first approach [3][4][5][6] deals with fiber-preserving transformations…”
Section: Introductionmentioning
confidence: 99%
“…Let I = I (x, p) be a smooth function on R2 x R 1 . In terms of the definition of conserved quantities in stochastic dynamical systems proposed by the author [12], the function becomes a conserved quantity for stochastic Hamilton dynamical system (1), if it satisfies…”
Section: A Stochastic Hamilton Dynamical Systemmentioning
confidence: 99%
“…Indeed, in stochastic dynamical systems mentioned above, the notion has been formulated in the various ways (e.g. [9,12,14]). Moreover, in the field of numerical analysis for deterministic dynamical systems described by ordinary differential equations, it is also recognized that the studies on the numerical preservation of the conserved quantities for dynamical systems are very important in performing reliable numerical calculations to the systems [5,7].…”
Section: Introductionmentioning
confidence: 99%
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“…First, restricted cases of point transformations were considered [1,10,16,17]. Then, the theory for general point transformations was developed [8,9,[25][26][27].…”
Section: Introductionmentioning
confidence: 99%