Nonlinear trend exclusion procedure for models defined by stochastic differential and difference equations
- 21 Downloads
We consider a diffusion process and its approximation with a Markov chain whose trends contain a nonlinear unbounded component. The usual parametrix method is inapplicable here since the trend is unbounded. We present a procedure that lets us exclude a nonlinear growing trend and pass to a stochastic differential equation with bounded drift and diffusion coefficients. A similar procedure is also considered for a Markov chain.
Keywordsstochastic differential equation diffusion process Markov chains parametrix method
Unable to display preview. Download preview PDF.
- 4.Konakov, V.D., The Parametrix Method for Diffusions and Markov Chains, Preprint, Moscow: Izd. Popech. Soveta Mekhaniko-Matematicheskogo Fakul’teta MGU, Ser. WP BRP “STI,”2012.Google Scholar
- 5.Arnol’d, V.I., Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow: Nauka, 1971.Google Scholar
- 6.Bibikov, Yu.N., Kurs obyknovennykh differentsial’nykh uravnenii (A Course in Ordinary Differential Equations), Moscow: Vysshaya Shkola, 1991.Google Scholar
- 7.Daletskii, Yu.L. and Krein, M.G., Ustoichivost’ reshenii differentsial’nykh uravnenii v banakhovom prostranstve (Stability of Solutions for Differential Equations in a Banach Space), Moscow: Nauka, 1970.Google Scholar
- 8.Kelley, W. and Peterson, A., The Theory of Differential Equations, Classical and Qualitative, Upper Saddle River: Prentice Hall, 2004.Google Scholar