Cover Image

On random measures on spaces of trajectories and strong and weak solutions of stochastic equations

We investigate stationary random measures on spaces of sequences or functions. A new definition of a strong solution of a stochastic equation is proposed. We prove that the existence of a weak solution in the ordinary sense is equivalent to the existence of a strong measure-valued solution.

Saved in:

Bibliographic Details
Date:	2004
Main Authors:	Dorogovtsev, A. A., Дороговцев, А. А.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 2004
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3782
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Stochastic Integrals with Respect to Consistent Random Measures
by: Dorogovtsev, A. A., et al.
Published: (2000)

On Stability of Solutions of a Stochastic Equation
by: Dorogovtsev, A. Ya., et al.
Published: (2004)

Stochastic integration and one class of Gaussian random processes
by: Dorogovtsev, A. A., et al.
Published: (1998)

Measure-Valued Markov Processes and Stochastic Flows
by: Dorogovtsev, A. A., et al.
Published: (2002)

On one condition of weak compactness of a family of measure-valued processes
by: Dorogovtsev, A. A., et al.
Published: (2004)

Stationary and periodic solutions of the operator Riccati equation under a random perturbation
by: Dorogovtsev, A. Ya., et al.
Published: (1993)

Visiting measures and an ergodic theorem for a sequence of iterations with random perturbations
by: Dorogovtsev, A. A., et al.
Published: (1999)

Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces
by: Dorogovtsev, A. A., et al.
Published: (2000)

Stochastic analysis and one minimization problem
by: Dorogovtsev, A. A., et al.
Published: (1994)

Asymptotic behaviour of the solution of Cauchy’s problem for stochastic equation of parabolic type
by: Dorogovtsev , A. Ya., et al.
Published: (1988)

Some characteristics of sequences of iterations with random perturbations
by: Dorogovtsev, A. A., et al.
Published: (1996)

On periodic and bounded solutions of the operator Riccati equation
by: Dorogovtsev, A. Ya., et al.
Published: (1993)

Weak invariance principle for solutions of stochastic recurrence equations in a banach space
by: Koval, V. A., et al.
Published: (1995)

The existence almost certainly strong solution of nonlinear stochastic functional differential equations with random perturbations
by: V. K. Yasynskyi, et al.
Published: (2016)

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)

On One Case of Existence of Homogeneous Solutions
by: Dorogovtsev, A. Ya., et al.
Published: (2002)

Homogenization of random functionals on solutions of stochastic equations
by: Ja. I. Granovskij, et al.
Published: (2015)

On weak convergence of solutions of random perturbed evolution equations
by: Kolomiets, Yu. V., et al.
Published: (1995)

Strong measurable continuous modifications of stochastic flows
by: O. Raimond, et al.
Published: (2023)

Strong measurable continuous modifications of stochastic flows
by: Raimond, Olivier, et al.
Published: (2023)

Kontsevich Integral Invariants for Random Trajectories
by: Kuznetsov, V. A., et al.
Published: (2015)

On the strong uniqueness of a solution to singular stochastic differential equations
by: O. V. Aryasova, et al.
Published: (2011)

Bounded solutions of one class of nonlinear operator difference equations
by: Gorodnii, M. F., et al.
Published: (1995)

Kontsevich Integral Invariants for Random Trajectories
by: V. A. Kuznetsov
Published: (2015)

The decomposition of a solution of the quasilinear stochastic parabolic equation with weak source
by: Melnik, S.
Published: (2007)

On the application of strong approximation to weak convergence of products of sums for dependent random variables
by: Matuła, P., et al.
Published: (2008)

Stochastic differential equation in a random environment
by: Ja. Makhno, et al.
Published: (2017)

Approximation of solutions of stochastic differential equations with fractional Brownian motion by solutions of random ordinary differential equations
by: Ral’chenko, K. V., et al.
Published: (2010)

Regularity of the mild solution of a parabolic equation with stochastic measure
by: I. M. Bodnarchuk
Published: (2017)

Weakly Sub-Gaussian Random Elements in Banach Spaces
by: Vakhaniya, N. N., et al.
Published: (2005)

Regularity of the mild solution of a parabolic equation with stochastic measure
by: Bodnarchuk, I. M., et al.
Published: (2017)

Some remarks on a Wiener flow with coalescence
by: Dorogovtsev, A. A., et al.
Published: (2005)

The existence of strong solutions of diffusion stochastic differential equations with entire prehistory and integral contractors
by: V. K. Yasynskyi, et al.
Published: (2013)

An example of a stochastic differential equation with the property of weak non-uniqueness of a solution
by: Kopytko, B.I., et al.
Published: (2006)

On asymptotic normality of the least square estimators of an infinite-dimensional parameter
by: Dorogovtsev, A. Ya., et al.
Published: (1993)

On weak convergence of stochastic differential equations with irregular coefficients
by: I. H. Krykun
Published: (2023)

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)

Mean-square asymptotic stability of solutions of systems of stochastic differential equations with random operators
by: Yurchenko, I. V., et al.
Published: (1995)

On strong existence and continuous dependence for solutions of one-dimensional stochastic equations with additive Levy noise
by: Yu. Pilipenko
Published: (2012)

One class of multidimensional stochastic differential equations having no property of weak uniqueness of a solution
by: Aryasova, O.V., et al.
Published: (2005)