Geodesic
Stochastic Differential Equations Driven by Generalized Positive Noise
Publications de l'Institut Mathématique, _N_S_77 (2005) no. 91, p. 7
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We consider linear SDEs with the generalized positive noise process standing for the noisy term. Under certain conditions, the solution, a Colombeau generalized stochastic process, is proved to exist. Due to the blowing-up of the variance of the solution, we introduce a ``new" positive noise process, a renormalization of the usual one. When we consider the same equation but now with the renormalized positive noise, we obtain a solution in the space of Colombeau generalized stochastic processes with both, the first and the second moment, converging to a finite limit.
DOI : 10.2298/PIM0591007O
Classification : 46F30 60G20 60H10 
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     title = {Stochastic {Differential} {Equations} {Driven} by {Generalized} {Positive} {Noise}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {7 },
     year = {2005},
     volume = {_N_S_77},
     number = {91},
     doi = {10.2298/PIM0591007O},
     zbl = {1112.46034},
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Michael Oberguggenberger; Danijela Rajter-Ćirić. Stochastic Differential Equations Driven by Generalized Positive Noise. Publications de l'Institut Mathématique, _N_S_77 (2005) no. 91, p. 7 . doi: 10.2298/PIM0591007O

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