On global in time solutions of stochastic algebraic-differerential equations with forward mean derivatives
Бесплатный доступ
The paper is devoted to the investigation of the completeness property of the flows generated by the stochastic algebraic-differential equations given in terms of forward Nelson's mean derivatives. This property means that all solutions of those equations exist for all t. It is very important for the description of qualitative behavior of the solutions. This problem is new since previously it was investigated for equations given in terms of symmetric mean derivatives. The case of forward mean derivatives requires different methods of investigation and the cases of forward and symmetric mean derivatives have different important applications. We find conditions under which all solutions of stochastic algebraic-differential equations given in terms of forward Nelson's mean derivatives, exist for all t. Some obtained conditions are necessary and sufficient.
Algebraic-differebtial equations, forvard mean derivatives, global in time solutions
Короткий адрес: https://sciup.org/147244582
IDR: 147244582 | DOI: 10.14529/mmp240208
Список литературы On global in time solutions of stochastic algebraic-differerential equations with forward mean derivatives
- Nelson, E. Derivation of the Schrodinger Equation from Newtonian Mechanics / E. Nelson // Physic Reviews. - 1966. - V. 150, № 4. - P. 1079-1085.
- Nelson, E. Dynamical Theory of Brownian Motion / E. Nelson. - Princeton: Princeton University Press, 1967.
- Nelson, E. Quantum Fluctuations / E. Nelson. - Princeton: Princeton University Press, 1985.
- Azarina, S.V. Differential Inclusions with Mean Derivatives / S.V. Azarina, Yu.E. Gliklikh // Dynamic Systems and Applications. - 2007. - V. 16, № 1. - P. 49-71.
- Gliklikh, Yu.E. Global and Stochastic Analysis with Applications to Mathematical Physics / Yu.E. Gliklikh. - London: Springer, 2011.
- Gliklikh, Yu.E. On Conditions for Completeness of Flows Generated by Stochastic Differential-Algebraic Equations / Yu.E. Gliklikh, D. Sergeeva // Global and Stochastic Analysis. - 2021. - V. 8, № 2. - P. 1-7._
- Чистяков, В.Ф. Избранные главы теории алгебро-дифференциальных систем / В.Ф. Чистяков, А.А. Щеглова. - Новосибирск: Наука, 2003.
- Партасарати, К. Введение в теорию вероятностей и теорию меры / К. Партасарати. -М.: Мир, 1983
- Elworthy K.D. Stochastic Differential Equations on Manifolds / K.D. Elworthy // Lecture Notes in Statistics. - Cambridge: Cambridge University Press, 1982.
- Gliklikh, Yu.E. Necessary and Sufficient Conditions for Global in Time Existence of Solutions of Ordinary, Stochastic, and Parabolic Differential Equations / Yu.E. Gliklikh // Abstract and Applied Analysis. - 2006. - V. 2006. - Article ID: 39786. - 17 p.
- Gliklikh, Yu.E. On the Completeness of Stochastic Flows Generated by Equations with Current Velocities / Yu.E. Gliklikh, T.A. Shchichko // Theory of Probability and its Applications. - 2019. - V. 64, № 1. - 11 p.
