Results 1 to 10 of about 10,118 (268)

Exponential integrators for stochastic Schrödinger equations [PDF]

Physical Review E, 2020
We present a class of exponential integrators to compute solutions of the stochastic Schr dinger equation arising from the modeling of open quantum systems. In order to be able to implement the methods within the same framework as the deterministic counterpart, we express the solution using the Kunita's representation.
Jingze Li, Xiantao Li
openaire   +3 more sources

Mathematical modeling and nonlinear bilateral multivalued stochastic integral equations [PDF]

PLoS ONE
Marek T. Malinowski
doaj   +2 more sources

A singular stochastic integral equation [PDF]

Proceedings of the American Mathematical Society, 1982
This note is devoted to the discussion of the stochastic differential equation X d X + Y d Y = 0 XdX + YdY = 0 , X X and Y Y being continuous local martingales. A method to construct solutions of this equation is given.
Nualart, David, Sanz, Marta
openaire   +4 more sources

Stochastic Integral Equations without Probability [PDF]

Bernoulli, 2000
L. C. Young has constructed an extension of the Riemann-Stieltjes integral \(\int_a^b f dh\), where the functions \(f,h:[a,b]\to{\mathbb R}\) have finite \(p\)-variation and finite \(q\)-variation, respectively, with \(p^{-1}+q^{-1}>1\). Motivated by the fact that certain stochastic processes which are not semimartingales may have a bounded \(p ...
Thomas Mikosch, Rimas Norvaiša, Rimas Norvaisa   +2 more
openaire   +3 more sources

On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions

Mathematics, 2021
It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering.
Ahmed M. A. El-Sayed, Hoda A. Fouad
doaj   +1 more source

Set-Valued Stochastic Lebesque Integral and Representation Theorems [PDF]

International Journal of Computational Intelligence Systems, 2008
In this paper, we shall firstly illustrate why we should introduce set-valued stochastic integrals, and then we shall discuss some properties of set-valued stochastic processes and the relation between a set-valued stochastic process and its selection ...
Jungang Li, Shoumei Li
doaj   +1 more source

On a Coupled System of Stochastic It$\widehat{o}$-Differential and the Arbitrary (Fractional) Order Differential Equations with Nonlocal Random and Stochastic Integral Conditions

Mathematics, 2021
The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance.
A. M. A. El-Sayed, Hoda A. Fouad
doaj   +1 more source

Representation of the Solution of Goursat Problem for Second Order Linear Stochastic Hyperbolic Differential Equations

Известия Иркутского государственного университета: Серия "Математика", 2021
The article considers second-order system of linear stochastic partial differential equations of hyperbolic type with Goursat boundary conditions. Earlier, in a number of papers, representations of the solution Goursat problem for linear stochastic ...
K.B. Mansimov, R.O. Mastaliyev
doaj   +1 more source

Martingale Decomposition and Backward Stochastic Dynamic Equations on Time Scales

Journal of Mathematics, 2022
The paper aims to establish the related backward stochastic dynamic equations on time scales, BS ∇ Es for short, concerning to ∇-integral on time scales.
Guofeng Tang, Guangyan Jia
doaj   +1 more source

Studying Some Stochastic Differential Equations with trigonometric terms with Application

Zanco Journal of Pure and Applied Sciences, 2022
In this paper we look at several (trigonometric) stochastic differential equations, we find the general form for such nonlinear stochastic differential equation by using the I'to formula.
Abdulghafoor Jasim Salim , Ali A. Asmael
doaj   +1 more source