Results 231 to 240 of about 315,767 (274)

Stochastic Differential Equations

1990
A stochastic (ordinary) differential equation (SDE) usually looks like this $$d{X^i}(t) = {\mu _i}(t,X(t))dt + \sum\limits_{j = 1}^d {{\sigma _{ij}}(t,X(t))d{B^j}(t),\quad 1 \leqslant i \leqslant n.} $$ (11.0.1)
Heinrich von Weizsäcker, Gerhard Winkler   +1 more
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Stochastic differential equations

Stochastic differential equations serve as the foundation for many sections of applied sciences, such as mechanics, statistical physics, diffusion theory, cosmology, financial mathematics, economics, etc. The number of works devoted to various issues related to specific equations considered in individual areas of science listed above is very large.
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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
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Stochastic Differential Equations

1991
In previous chapters stochastic differential equations have been mentioned several times in an informal manner. For instance, if M is a continuous local martingale, its exponential e(M) satisfies the equality $$\mathcal{E}{(M)_t} = 1 + \int_0^t {\mathcal{E}{{(M)}_s}} d{M_s};$$ this can be stated: e(M) is a solution to the stochastic differential
Daniel Revuz, Marc Yor
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Stochastic Differential Equations

2017
In this chapter we establish the well-posedness and a priori estimates for SDEs. Weak solutions of SDEs will also be studied briefly.
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Strong convergence of a Euler-Maruyama scheme to a variable-order fractional stochastic differential equation driven by a multiplicative white noise

Chaos, Solitons and Fractals, 2021
zhiwei yang, Xiangcheng Zheng, Zhongqiang Zhang   +2 more
exaly  

Solvability and optimal controls of non-instantaneous impulsive stochastic fractional differential equation of order q ∈ (1,2)

Stochastics, 2021
Rajesh Dhayal, Muslim Malik, Syed Abbas
exaly  

Stochastic Differential Equations

2009
The chapter begins with Section 4.1 in which motivational examples of random walks and stochastic phenomena in nature are presented. In Section 4.2 the concept of random processes is introduced in a more precise way. In Section 4.3 the concept of a Gaussian and Markov random process is developed. In Section 4.4 the important special case of white noise
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The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm

Stochastic Analysis and Applications, 2021
Xiao-Bao Shu, Fei Xu
exaly  

On stochastic differential equations

Memoirs of the American Mathematical Society, 1951
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