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Stochastic Functional Differential Equation under Regime Switching [PDF]

Discrete Dynamics in Nature and Society, 2012
We discuss stochastic functional differential equation under regime switching dx(t)=f(xt,r(t),t)dt+q(r(t))x(t)dW1(t)+σ(r(t))|x(t)|βx(t)dW2(t). We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its ...
Ling Bai, Zhang Kai
doaj   +2 more sources

Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility

Mathematics, 2016
We perform a classification of the Lie point symmetries for the Black-Scholes-Merton Model for European options with stochastic volatility, σ, in which the last is defined by a stochastic differential equation with an Orstein-Uhlenbeck term.
Andronikos Paliathanasis, K. Krishnakumar, K.M. Tamizhmani, Peter G.L. Leach   +3 more
doaj   +4 more sources

Almost Periodic Solutions to Impulsive Stochastic Delay Differential Equations Driven by Fractional Brownian Motion With 12 < H < 1

Frontiers in Physics, 2021
In this article, we study the existence and uniqueness of square-mean piecewise almost periodic solutions to a class of impulsive stochastic functional differential equations driven by fractional Brownian motion.
Lili Gao, Xichao Sun
doaj   +1 more source

Hypercontractivity for functional stochastic differential equations [PDF]

Stochastic Processes and their Applications, 2015
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup $P_t$ converges exponentially to its unique invariant probability measure $ $ in entropy, $L^2( )$ and the totally variational norm, and it is compact in $L^2(
Bao, Jianhai, Wang, Feng-Yu, Yuan, Chenggui   +2 more
openaire   +4 more sources

Closed-Loop Solvability of Stochastic Linear-Quadratic Optimal Control Problems with Poisson Jumps

Mathematics, 2022
The stochastic linear–quadratic optimal control problem with Poisson jumps is addressed in this paper. The coefficients in the state equation and the weighting matrices in the cost functional are all deterministic but are allowed to be indefinite.
Zixuan Li, Jingtao Shi
doaj   +1 more source

A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations

Mathematics, 2022
This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Euler ...
Qi Wang, Huabin Chen, Chenggui Yuan
doaj   +1 more source

Indefinite Linear-Quadratic Stochastic Control Problem for Jump-Diffusion Models with Random Coefficients: A Completion of Squares Approach

Mathematics, 2021
In this paper, we study the indefinite linear-quadratic (LQ) stochastic optimal control problem for stochastic differential equations (SDEs) with jump diffusions and random coefficients driven by both the Brownian motion and the (compensated) Poisson ...
Jun Moon, Jin-Ho Chung
doaj   +1 more source

On Weak and Strong Solutions of Paired Stochastic Functional Differential Equations in Infinite-Dimensional Spaces

Journal of Optimization, Differential Equations and Their Applications, 2021
In this paper, we study the questions of the existence of global weak solutions and local strong solutions of paired stochastic functional differential equations in a Hilbert space, one of which is an equation with an unbounded operator, and the other is
Andrey O. Stanzhytskyi
doaj   +1 more source

Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

Advances in Difference Equations, 2021
This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms.
Abdulwahab Almutairi, H. El-Metwally, M. A. Sohaly, I. M. Elbaz   +3 more
doaj   +1 more source

Linear Quadratic Stochastic Differential Games: Open-Loop and Closed-Loop Saddle Points [PDF]

, 2014
In this paper, we consider a linear quadratic stochastic two-person zero-sum differential game. The controls for both players are allowed to appear in both drift and diffusion of the state equation.
Sun, Jingrui, Yong, Jiongmin
core   +3 more sources