5 citations · 7 across the 11 of their papers we have counts for
11 papers
Langevin equations with multiplicative noise: uniqueness, self-consistency and new solution methods by a time-discrete approach
Dietrich Ryter
A time-discrete approach avoids the assumption of an 'integration sense'. New path increments (in a short time step) are complete in the order of that step, and not Gaussian distri…
A maximum principle for the stochastic differential equations with multiplicative noise
Dietrich Ryter
Agreement of the probability current with the resolving paths requires a simplified forward equation for the (unique) Ito paths. Their increments are the most probable rather than…
Stochastic differential equations: loss of the Markov property by multiplicative noise
Dietrich Ryter
The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation…
The intrinsic "sense" of stochastic differential equations
Dietrich Ryter
A free choice of the integration sense would lead to the paradox that the number of possible equations (thus of solutions for a given model) can vary under a mere change of the var…
Stochastic differential equations with covariant probabilities
Dietrich Ryter
Covariance of the resulting probabilities requires the "anti-Ito" sense. The corresponding Fokker-Planck equation is simplified and preserves important features of the case with a…
Partial and full solutions of stochastic differential equations
Dietrich Ryter
Only the "anti-Ito" integral yields the correct shift of the mean, by the fact that the elements of its Riemannian sum hold in the order O(dt) rather than only in O(sqrt dt). The c…