Abstract
Existence and uniqueness theorems are given for RODEs under classical and Carathéodory assumptions. In the latter case the measurability of solutions is also established. Conditions ensuring the positivity of solutions are stated and RODEs with canonical noise are formulated.
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Notes
- 1.
Essentially, \(\{W_t, t\ge 0\}\), and \(\{W_{-t}, t\le 0\}\) are two independent Wiener processes.
- 2.
No other topological properties of the space \(\mathscr {C}_0(\mathbb {R},\mathbb {R})\) are used here apart from those defining the Borel sets.
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Han, X., Kloeden, P.E. (2017). Random Ordinary Differential Equations. In: Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling, vol 85. Springer, Singapore. https://doi.org/10.1007/978-981-10-6265-0_2
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DOI: https://doi.org/10.1007/978-981-10-6265-0_2
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6264-3
Online ISBN: 978-981-10-6265-0
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