Name
Abstract | ||
|---|---|---|
In this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d-dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the Aumann type set-valued Lebesgue integral of a set-valued stochastic process above is a set-valued stochastic process. Finally we shall give the representation theorem, and prove an important inequality of the Aumann type set-valued Lebesgue integrals of set-valued stochastic processes with respect to t, which are useful to study set-valued stochastic differential inclusions with applications in finance. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.2991/jnmp.2009.2.1.9 | INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS |
Keywords | Field | DocType |
set-valued stochastic process, set-valued Lebesgue integral, Aumann type integral, representation theorem | Riemann integral,Discrete mathematics,Mathematical optimization,Stratonovich integral,Representation theorem,Lebesgue–Stieltjes integration,Stochastic differential equation,Daniell integral,Lebesgue's number lemma,Mathematics,Lebesgue integration | Journal |
Volume | Issue | ISSN |
2 | 1 | 1875-6891 |
Citations | PageRank | References |
4 | 0.48 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jungang Li | 1 | 19 | 4.91 |
| Shoumei Li | 2 | 205 | 49.34 |