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This is a literature study of strong solutions and weak solutions of a stochastic differential equation. For the purpose, we study probability theory which underlies the subject: stochastic processes, filtration, Brownian motion, Ito integral and stochastic differential equations. We also compare co...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/11182 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This is a literature study of strong solutions and weak solutions of a stochastic differential equation. For the purpose, we study probability theory which underlies the subject: stochastic processes, filtration, Brownian motion, Ito integral and stochastic differential equations. We also compare condition for existence and uniqueness of solution to an ordinary differential equation and that of stochastic differential equation.<p> <br />
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The main difference of strong solutions and weak solutions is their measurability with respect to the filtration generated by the given Brownian motion. A strong solution must solve the differential equation, and at the same time must be measurable with respect to the filltration; while a weak solution has only to satisfy the differential equation. Tanaka equation gives an example of a stochastic differential equation with only a weak solution, without a strong one. |
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