LEISURE RANDOM WALK
A random walk in n-dimensional lattice, Z^n is a step by step walk with direction taken at random walk independently. In one dimension the direction are left and right, in two dimension we have left, right, up and down directions, and so on. <br /> <br /> <br /> <br /> A s...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/21471 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A random walk in n-dimensional lattice, Z^n is a step by step walk with direction taken at random walk independently. In one dimension the direction are left and right, in two dimension we have left, right, up and down directions, and so on. <br />
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A standard symetric random walk in one dimension, technically is a sequence of random variable X_i (i=1,2,⋯) with value ±1, each with probability 1/2. A leisure random walk in one dimension is a three valued sequence of random variable X_i= -1,0,+1, each with probability 1/3. The addition of 0 can be interpreted as the option of not stepping (stopping). <br />
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For a simple random walk the typical position of a random walker after n-steps is √n. For a leisure random walk the typical distance is √(2/3 n). Similar to simple random walk, leisure random walk can be used for representing a solution of boundary value problem. By scaling limit, leisure random walk will convergent to leisure Brownian motion with normal distribution N(0,2/3 t). <br />
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