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boliobolo
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can someone show me the solution for E[B(u)B(u+v)B(u+v+w)B(u+v+w+x)], for 0<u<u+v<u+v+w<u+v+w+x .the answer is 3u^2+3uv+uw
Brownian motion is the random movement of particles in a fluid, caused by collisions with other particles in the fluid. It was first observed by the botanist Robert Brown in the early 19th century.
Brownian motion occurs due to the random thermal motion of particles in a fluid. As these particles move and collide with each other, they cause other particles to move in a random pattern.
Brownian motion is important in many areas of science, including physics, chemistry, and biology. It provides evidence for the existence of atoms and molecules, and is used to study diffusion and other processes in fluids.
Brownian motion is closely related to the concept of entropy, which is a measure of the disorder or randomness in a system. The random movement of particles in Brownian motion increases the entropy of a system.
Yes, Brownian motion can be observed in many everyday phenomena. For example, the random movement of particles in a cup of tea or coffee is a result of Brownian motion. It is also seen in the movement of dust particles in the air or the diffusion of perfume in a room.