Results 271 to 280 of about 50,968 (311)

ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Mathematics of the USSR-Sbornik, 1975
In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
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The Magnus Expansion for Stochastic Differential Equations

Journal of Nonlinear Science, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhenyu Wang, Qiang Ma 0004, Zhen Yao, Xiaohua Ding   +3 more
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Stochastic partial differential equations

2014
Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
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Stochastic differential equations and applications

2008
This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and ...
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On a Class of Stochastic Differential Equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1963
AbstractStochastic differential equations of the type dy/dt + A(t) y = x(t) (A(t) being a matrix) are studied on the assumption that the random element is introduced only through x(t). Any component xi(t) of x(t) is characterised by the fact that in any finite interval (0,t) it undergoes only a finite number of discrete transitions, xi(t) remaining a ...
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Stochastic Differential Equations

2014
Stochastic differential equations describe the time evolution of certain continuous n-dimensional Markov processes. In contrast with classical differential equations, in addition to the derivative of the function, there is a term that describes the random fluctuations that are coded as an Ito integral with respect to a Brownian motion. Depending on how
Gopinath Kallianpur, P. Sundar
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Stochastic Differential Equations

2012
Stochastic differential equations arise when modeling prices of financial instruments, a variety of physical systems, and in many other branches of science. As we shall see in the next section, there is a deep relationship between stochastic differential equations and linear elliptic and parabolic partial differential equations.
Leonid Koralov, Yakov G. Sinai
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Stochastic Differential Equations

2021
The concept of a Langevin equation was introduced in Sec. 6.1.1 as the equation of motion of a particle subject to a rapidly fluctuating force. There we treated the Langevin source ξ(t) as a stochastic function with a very short correlation time, and developed results that would be valid in the limit that this correlation time becomes zero.
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Stochastic differential equations

2009
Consider a complete filtration \({\mathcal{F}}_t\), t∈[0,T]} and an m-dimensional Wiener process {W(t), t ∈ [0,T]} with respect to it. By definition, a stochastic differential equation (SDE) is an equation of the form with X 0=ξ, where ξ is an \({\mathcal{F}}_0\)-measurable random vector, \(b=b(t,x): [0,T]\times \mathbb{R}^n\rightarrow \mathbb{R}^n ...
Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko   +4 more
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Some results on the study of Caputo–Hadamard fractional stochastic differential equations

Chaos, Solitons and Fractals, 2022
Abdellatif Ben Makhlouf, Lassaad Mchiri
exaly