Probability Distribution Notes: Probability is a fundamental aspect of mathematics that helps us understand and quantify uncertainty. Mastery of this subject is essential for students, as it has ...

All sorts of physical processes in this analog world exhibit some degree of randomness. Think of noise, for example. Many noisy processes are described by Gaussian probability distributions. We should ...

The `point quadrat' is a sharp needle inserted into vegetation, contacts between needle and foliage surfaces being counted. Refinement of established botanical techniques, based on the absence of ...

We construct weak solutions to the McKean–Vlasov SDE dX( t )=b( X( t ), d L X( t ) dx ( X( t ) ) )dt+σ( X( t ), d L X( t ) dt ( X( t ) ) )dW( t ) on ℝd for possibly degenerate diffusion matrices σ ...

One of the characteristic features of classical chaos is the evolution of the small-scale structure in phase-space probability distributions. As a consequence of the exponential sensitivity to initial ...