[Derivation Scribbles] Exact Solution to a Multivariate OU Process
Derivation Scribbles
Stochastic Calculus
Exact solution to a multivarite Ornstein-Uhlenbeck process.
[Derivation Scribbles] Probabilistic ODE Solvers
Derivation Scribbles
Data Assimilation
Gaussian Process
Probabilistic Numerics ODE Solver
[Derivation Scribbles] Fourier Transform and FFT
Derivation Scribbles
Describes the Fourier transform, mentions the sampling theorem that connects discrete and continuous time Fourier transform, and presents the fast Fourier transform that efficiently applies the discrete Fourier transform to a uniformly sampled sequence.
Upscale a Brownian Motion Path
Gaussian Process
Sampling
Stochastic Calculus
For a Brownian motion path observed at fixed locations, upscale the resolution using conditioning using the fact that a Brownian motion is a Gaussian process.
Summary of a Bivariate Gaussian Covariance Matrix
Active Learning
Gaussian Process
Various ways one could summarise a bivariate Gaussian’s covariance matrix.
[Derivation Scribbles] 3D-Var and 4D-Var
Data Assimilation
Derivation Scribbles
Derivations for 3D-Var and 4D-Var.
[Derivation Scribbles] Kalman Filter and Ensemble Kalman Filter
Data Assimilation
Derivation Scribbles
Derivations for Kalman filters and Ensemble Kalman Filter.
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