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The quadratic process is expanded according to the Kac-Siegert method.
Quadratic process order has been selected for regression analysis of the experimental data as analyzed by ANOVA.
This study deals with the problem of the extreme distribution of a stationary non-Gaussian translation process which is a memoriless deterministic transformation of a linear and a pure quadratic process.
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A statistical method used for estimating the linear and quadratic processes in laboratory plasma is adapted for dispersive waves in space plasma turbulence.
This is because Markov chains are discontinuous stochastic processes with finite variation and the quadratic processes of the martingales generated by Markov chains are quite different from the continuous-time diffusions.
Its quadratic variation process is also a continuous process with independent and stationary increments.
A very interesting phenomenon of G-Brownian motion is that its quadratic variation process is also a continuous process with independent and stationary increments, and thus can still be regarded as a Brownian motion.
The quadratic variation process 〈W〉 t is also a continuous process with independent and stationary increments.
Note that the predictable quadratic variation process (langle Y,p(x rangle _{s}^{mathbb {F},mathbb {P}}) vanishes on [ [0,τ] ] since the process Y begins at τ. Hence, int_{]0,t]}frac{dlangle Y,p(x rangle_s^{mathbb{F},mathbb{P}}}{p_{s-}(x)}=mathbb{1}_{{tauleq t}}int_{]0,t]}frac{dlangle Y,p(x rangle_s^{mathbb{F},mathbb{P}}}{p_{s-}(x)}.
where the square brackets denote the quadratic variation process.
where W t is a G-Brownian motion and 〈W〉 t is its quadratic variation process.
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