Cover Image

On the existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process

We study the problem of existence and uniqueness of a solution of a linear stochastic differential equation with respect to a logarithmic process. For the conditional mathematical expectation of a solution, we obtain a partial differential equation.

Saved in:

Bibliographic Details
Date:	1997
Main Authors:	Pilipenko, A. Yu., Пилипенко, А. Ю.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 1997
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/5075
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

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

On the properties of an operator of stochastic differentiation constructed on a group
by: Pilipenko, A. Yu., et al.
Published: (1996)

The law of iterated logarithm for solutions of stochastic differential equations
by: Makhno, S. Ya., et al.
Published: (1996)

Existence and Uniqueness of the Solution of a Stochastic Partial Functional Differential Equation of a Special Form and Methods of its Computer Modeling
by: Юрченко, Ігор, et al.
Published: (2025)

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)

Transfer of absolute continuity by a flow generated by a stochastic equation with reflection
by: Pilipenko, A. Yu., et al.
Published: (2006)

Existence and uniqueness of solution to the Cauchy problem for neutral stochastic differential equation of reaction-diffusion type
by: A. N. Stanzhitskij, et al.
Published: (2016)

Conditions for the existence and uniqueness of bounded solutions of nonlinear differential equations
by: Slyusarchuk, V. Yu., et al.
Published: (2009)

Existence, uniqueness, and estimation of solutions for a set of equations of perturbed motion
by: Martynyuk, A. A., et al.
Published: (2013)

On the strong existence and uniqueness to a solution of a countable system of SDEs with measurable drift
by: A. Pilipenko, et al.
Published: (2014)

Existence and uniqueness of solution of mixed stochastic differential equation driven by fractional Brownian motion and wiener process
by: Mishura, Y., et al.
Published: (2007)

Stroock–Varadhan Theorem for Flows Generated by Stochastic Differential Equations with Interaction
by: Pilipenko, A. Yu., et al.
Published: (2002)

General Theorems on the Existence and Uniqueness of Solutions of Impulsive Differential Equations
by: Slyusarchuk, V. E., et al.
Published: (2000)

Existence and asymptotic properties of solutions of a real system of differential equations unresolved with respect to the derivative
by: Prosenyuk, L. G., et al.
Published: (1993)

Existence, uniqueness, and dependence on a parameter of solutions of differential-functional equations with ordinary and partial derivatives
by: Bigun, Ya. I., et al.
Published: (1997)

Asymptotics of the fundamental system of solutions of a linear functional-differential equation with respect to a parameter
by: Radzievskii, G. V., et al.
Published: (1995)

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

On the existence of unique solutions of linear matrix equations over rings with involution
by: V. R. Zelisko, et al.
Published: (2015)

Stochastic differential equations with interaction and the law of iterated logarithm
by: M. P. Lagunova
Published: (2012)

Existence, uniqueness, and estimation of solutions for a set of equations of perturbed motion
by: A. A. Martynjuk, et al.
Published: (2013)

Uniqueness in law of solutions of stochastic differential inclusions
by: Lepeyev, A.N.
Published: (2007)

On the existence and uniqueness of the solution of a differential equation with interaction governed by generalized function in abstract wiener space
by: Brayman, V.B.
Published: (2005)

Malmquist theorem for solutions of differential equations in a neighborhood of a logarithmic singular point
by: Mokhonko, A. A., et al.
Published: (2004)

Asymptotics of Polynomials Orthogonal with respect to a Logarithmic Weight
by: Conway, T.O., et al.
Published: (2018)

Properties of the Flows Generated by Stochastic Equations with Reflection
by: Pilipenko, A. Yu., et al.
Published: (2005)

Existence and uniqueness of solution of the Cauchy problem for singular systems of integro-differential equations
by: Shmarda, Z., et al.
Published: (1993)

On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point
by: Mokhonko, A. Z., et al.
Published: (2003)

A criterion for the existence of the unique invariant torus of a linear extension of dynamical systems
by: Boichuk, О. A., et al.
Published: (2007)

On the Existence of a Unique Green Function for the Linear Extension of a Dynamical System on a Torus
by: Samoilenko, A. M., et al.
Published: (2001)

Limit theorem for coiuntable systems of stochastic differential equations
by: Pilipenko, A. Yu., et al.
Published: (2016)

Time-Irreversibility and Existence and Uniqueness of Solutions of Problems in Linear Viscoelasticity
by: Matarazzo, G.
Published: (2000)

Time-Irreversibility and Existence and Uniqueness of Solutions of Problems in Linear Viscoelasticity
by: Matarazzo, G., et al.
Published: (2000)

Conditions of smoothness for the distribution density of a solution of a multidimensional linear stochastic differential equation with levy noise
by: Bodnarchuk, S. V., et al.
Published: (2011)

On the existence and uniqueness of a solution of the problem of uniform SK-spline-interpolation
by: Serdyuk, A. S., et al.
Published: (1999)

Conditions for the existence of basic solutions of linear multivalued differential equations
by: Komleva, T. A., et al.
Published: (2021)

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

Existence of a solution to the Dirichlet problem for the heat equation with general stochastic measure
by: M. F. Horodnii
Published: (2018)

Existence of a solution of the Neumann problem for the heat equation with general stochastic measure
by: M. F. Horodnii, et al.
Published: (2015)

Existence and uniqueness of solution to a parabolic-hyperbolic equation with multiplicative control and nonlocally boundary conditions
by: V. Kapustyan, et al.
Published: (2024)

On the existence, uniqueness, and nonexistence of solutions of one boundary-value problem for a semilinear hyperbolic equation
by: S. Kharibegashvili, et al.
Published: (2019)