Strong Markov continuous local martingales and solutions of one- dimensional stochastic differential equations. III. (English) Zbl 0731.60053

Engelbert, H. J.; Schmidt, W.

Math. Nachr. 151, 149-197 (1991).

This is the third part of a deep study by the same authors [see ibid. 143, 167-184 (1989; Zbl 0699.60044) and the paper reviewed above], the concern here being with one-dimensional stochastic differential equations driven by a Wiener process. Section 4, the first section of this paper, provides a survey on existence, uniqueness and other aspects of solutions, while Section 5 discusses conditions under which a strong Markov continuous local martingale is a solution of a one-dimensional stochastic differential equation without drift.

Reviewer: A.Dale (Durban)

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60G44	Martingales with continuous parameter
34F05	Ordinary differential equations and systems with randomness

Keywords:

stochastic differential equations; survey on existence, uniqueness and other aspects of solutions; strong Markov continuous local martingale

Citations:

Zbl 0731.60052; Zbl 0699.60044

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