Stability with probability I for solutions of linear stochastic differential-difference Ito’s equations
Conditions for absolute (independent of lags) asymptotic stability with probability 1 of systems of stochastic equations cited in the title of this paper are obtained. The proposed approach allows us to reduce the problem of analyzing stability to determination of the conditions for the existence of...
Saved in:
| Date: | 2025 |
|---|---|
| Main Authors: | Zelentsovsky , A. L., Зеленцовский , A. Л. |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/9347 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: | |
Institution
Ukrains’kyi Matematychnyi ZhurnalSimilar Items
The existence of Lyapunov–Krasovskii functionals for stochastic differential-functional Ito–Skorokhod equations under the condition of the solutions stability on probability with finite aftereffect
by: I. V. Jurchenko, et al.
Published: (2018)
by: I. V. Jurchenko, et al.
Published: (2018)
Asymptotic equivalence of the solutions of the linear stochastic ito equations in the Hilbert space
by: Krenevych, A.
Published: (2007)
by: Krenevych, A.
Published: (2007)
Asymptotic equivalence of solutions of linear Itô stochastic systems
by: Krenevych, A. P., et al.
Published: (2006)
by: Krenevych, A. P., et al.
Published: (2006)
Stability after the first approaching of solutions of Ito-Schorohod's stochastic differential equations in Hilbert spaces
by: A. V. Nikitin, et al.
Published: (2013)
by: A. V. Nikitin, et al.
Published: (2013)
Qualitative Analysis of Systems of Itô Stochastic Differential Equations
by: Kulinich, G. L., et al.
Published: (2000)
by: Kulinich, G. L., et al.
Published: (2000)
On the stochastic stability of nonlinear systems with Ito zahayuvannyamy
by: A. M. Kalyniuk, et al.
Published: (2014)
by: A. M. Kalyniuk, et al.
Published: (2014)
On the stability of the solution of the linear autonomous stochastic partial differential equation with external random disturbances
by: V. K. Yasynskyi, et al.
Published: (2014)
by: V. K. Yasynskyi, et al.
Published: (2014)
Exponential Dichotomy and Mean Square Bounded Solutions of Linear Stochastic Ito Systems
by: Stanzhitskyi, O.M.
Published: (2001)
by: Stanzhitskyi, O.M.
Published: (2001)
On existence and stabization of the strong solution of the autonomous stochastic partial differential Ito–Skorokhod equation with random parameters
by: V. K. Yasynskyy, et al.
Published: (2018)
by: V. K. Yasynskyy, et al.
Published: (2018)
On the representation of solutions of anticipating linear partial stochastic differential equations
by: Ilchenko, A.V.
Published: (2007)
by: Ilchenko, A.V.
Published: (2007)
The construction of the stability domains of linear differential-difference equations
by: I. I. Klevchuk, et al.
Published: (2012)
by: I. I. Klevchuk, et al.
Published: (2012)
The local principle of large deviations for solutions of Ito stochastic equations with quick drift
by: A. V. Logachjov
Published: (2015)
by: A. V. Logachjov
Published: (2015)
On the stability of solutions of stochastic differential inclusions
by: Kravets, T. N., et al.
Published: (1995)
by: Kravets, T. N., et al.
Published: (1995)
On Stability of Solutions of a Stochastic Equation
by: Dorogovtsev, A. Ya., et al.
Published: (2004)
by: Dorogovtsev, A. Ya., et al.
Published: (2004)
Relationship between spectral and coefficient criteria of mean-square stability for systems of linear stochastic differential and difference equations
by: Korenevsky, D. G., et al.
Published: (2000)
by: Korenevsky, D. G., et al.
Published: (2000)
On the Asymptotic Properties of Solutions of Linear Stochastic Differential Equations in $R^d$
by: Buldygin, V. V., et al.
Published: (2000)
by: Buldygin, V. V., et al.
Published: (2000)
Asymptotic stability of solutions of systems of stochastic differential equations in the critical case
by: Yurchenko, I. V., et al.
Published: (1995)
by: Yurchenko, I. V., et al.
Published: (1995)
Criteria of the mean-square asymptotic stability of solutions of systems of linear stochastic difference equations with continuous time and delay
by: Korenevsky, D. G., et al.
Published: (1998)
by: Korenevsky, D. G., et al.
Published: (1998)
On Invariant Tori of Itô Stochastic Systems
by: Samoilenko, A. M., et al.
Published: (2002)
by: Samoilenko, A. M., et al.
Published: (2002)
On one attribute of solution stability for systems of non-linear differential equations
by: Martynyuk, A. A., et al.
Published: (1971)
by: Martynyuk, A. A., et al.
Published: (1971)
On the stability with probability one for a class of stochastic semigroups
by: Chani, A.C.
Published: (2005)
by: Chani, A.C.
Published: (2005)
Stability of linear systems of differential equations with random jumps linear solutions in Hilbert spaces
by: A. V. Nikitin
Published: (2014)
by: A. V. Nikitin
Published: (2014)
Stability of linear systems of differential equations with random jump linear solutions in Hilbert space
by: A. V. Nikitin
Published: (2013)
by: A. V. Nikitin
Published: (2013)
Stability of linear systems of differential equations with random jump linear solutions in Hilbert space
by: Nikitin, A.V.
Published: (2013)
by: Nikitin, A.V.
Published: (2013)
On the necessary and sufficient conditions of the stability in the mean square of the strong solutions of linear stochastic differential-difference partial derivative equations subject to external perturbations of the type of random variable
by: T. O. Lukashiv, et al.
Published: (2020)
by: T. O. Lukashiv, et al.
Published: (2020)
On time inhomogeneous stochastic Itô equations with drift in $L_{d+1}$
by: Krylov, N. V. , et al.
Published: (2020)
by: Krylov, N. V. , et al.
Published: (2020)
Mean-square asymptotic stability of solutions of systems of stochastic differential equations with random operators
by: Yurchenko, I. V., et al.
Published: (1995)
by: Yurchenko, I. V., et al.
Published: (1995)
Absolute asymptotic stability of solutions of linear parabolic differential equations with delay
by: Kushnir, V. P., et al.
Published: (2007)
by: Kushnir, V. P., et al.
Published: (2007)
Optimal control in diffusion stochastic nonlinear functional-differential Ito equations with Markov parameters and external markovian switching
by: V. K. Jasinskij, et al.
Published: (2016)
by: V. K. Jasinskij, et al.
Published: (2016)
Stochastic Stability of Processes Determined by Poisson Differential Equations with Delay
by: Svishchuk, A. V., et al.
Published: (2002)
by: Svishchuk, A. V., et al.
Published: (2002)
Solution of stochastic differential equation for control problem
by: K. G. Dzjubenko
Published: (2015)
by: K. G. Dzjubenko
Published: (2015)
On the Impossibility of Stabilization of Solutions of a System of Linear Deterministic Difference Equations by Perturbations of Its Coefficients by Stochastic Processes of “White-Noise” Type
by: Korenevsky, D. G., et al.
Published: (2002)
by: Korenevsky, D. G., et al.
Published: (2002)
On the existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process
by: Pilipenko, A. Yu., et al.
Published: (1997)
by: Pilipenko, A. Yu., et al.
Published: (1997)
On the stability and instability of solutions of linear differential equations of the $n$th order with periodic coefficients
by: Zadiraka, К. V., et al.
Published: (1966)
by: Zadiraka, К. V., et al.
Published: (1966)
On differentiability of solution to stochastic differential equation with fractional Brownian motion
by: Mishura, Yu.S., et al.
Published: (2007)
by: Mishura, Yu.S., et al.
Published: (2007)
Convergence of solutions of stochastic differential equations to the Arratia flow
by: Malovichko, T. V., et al.
Published: (2008)
by: Malovichko, T. V., et al.
Published: (2008)
The law of iterated logarithm for solutions of stochastic differential equations
by: Makhno, S. Ya., et al.
Published: (1996)
by: Makhno, S. Ya., et al.
Published: (1996)
Viability of solutions of many-dimensional stochastic differential equations
by: Gasanenko, V. A., et al.
Published: (1997)
by: Gasanenko, V. A., et al.
Published: (1997)
Stochastic stability of a class of partial differential equations of thermoelasticity
by: Krol, M.
Published: (2008)
by: Krol, M.
Published: (2008)
On the φ-asymptotic behaviour of solutions of stochastic differential equations
by: Buldygin, V.V., et al.
Published: (2008)
by: Buldygin, V.V., et al.
Published: (2008)
Similar Items
-
The existence of Lyapunov–Krasovskii functionals for stochastic differential-functional Ito–Skorokhod equations under the condition of the solutions stability on probability with finite aftereffect
by: I. V. Jurchenko, et al.
Published: (2018) -
Asymptotic equivalence of the solutions of the linear stochastic ito equations in the Hilbert space
by: Krenevych, A.
Published: (2007) -
Asymptotic equivalence of solutions of linear Itô stochastic systems
by: Krenevych, A. P., et al.
Published: (2006) -
Stability after the first approaching of solutions of Ito-Schorohod's stochastic differential equations in Hilbert spaces
by: A. V. Nikitin, et al.
Published: (2013) -
Qualitative Analysis of Systems of Itô Stochastic Differential Equations
by: Kulinich, G. L., et al.
Published: (2000)