Open AccessOn the approximations of solutions to stochastic differential equations under polynomial condition
Author(s) -
Dušan D. Djordjević,
Miljana Jovanović
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2101011d
Subject(s) - mathematics , lipschitz continuity , bounded function , stochastic differential equation , mathematical analysis , interval (graph theory) , polynomial , taylor series , rate of convergence , convergence (economics) , differential equation , class (philosophy) , combinatorics , economic growth , computer science , electrical engineering , economics , channel (broadcasting) , artificial intelligence , engineering
The subject of this paper is an analytic approximate method for a class of stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions but behave like a polynomials. More precisely, equations from the observed class have unique solutions with bounded moments and their coefficients satisfy polynomial condition. Approximate equations are defined on partitions of a time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. The rate of Lp convergence increases when degrees in Taylor approximations of coefficients increase. At the end of the paper, an example is provided to support the main theoretical result.