Convergence of solutions of one-dimensional stochastic equations (Q2711138)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Convergence of solutions of one-dimensional stochastic equations |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of solutions of one-dimensional stochastic equations |
scientific article |
Statements
2 May 2001
0 references
stochastic equations
0 references
limit theorems
0 references
necessary conditions of convergence
0 references
sufficient conditions of convergence
0 references
0.95014703
0 references
0.9485213
0 references
Convergence of solutions of one-dimensional stochastic equations (English)
0 references
The author considers one-dimensional stochastic equations NEWLINE\[NEWLINE\xi_\varepsilon(t)=x+\int_0^t [b_\varepsilon(\xi_\varepsilon(s))+g_\varepsilon(\xi_\varepsilon(s))] ds+ \int_0^t\sigma_\varepsilon(\xi_\varepsilon(s)) dw(s),NEWLINE\]NEWLINE the coefficients of which depend on a small parameter \(\varepsilon\) in an irregular way. Necessary and sufficient conditions are obtained for the weak convergence of \(\xi_\varepsilon(t)\) to \(\xi(t)\) which is a solution of the stochastic equation NEWLINE\[NEWLINE\xi(t)=x+\int_0^t B(\xi(s)) ds+\int_0^t\sigma(\xi(s)) dw(s). NEWLINE\]NEWLINE Four examples are considered.
0 references
