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A Levy process is a stochastic process with stationary, independent increments. These processes have a lot of structure - partly due to the Levy-Khintchine theorem. This says that the Fourier transform of the transition density of a Levy process has a particularly nice form, and has lead to many applications of fourier theory to finance.

All non-Brownian Levy processes have heavier tails than Brownian motion. They are semimartingales, and thus one can define a sensible notion of stochastic integration with respect to a Levy process. As such, they make nice models for log asset proce price processes, though they have many other applications in finance.

Take a look at Cont and Tankov's book - it's probably the friendliest introduction to Levy process I've seen. Other more theoretical books include those of Kyprianou, Applebaum and Sato (in approximate order of difficulty).

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A Levy process is a stochastic process with stationary, independent increments. These processes have a lot of structure - partly due to the Levy-Khintchine theorem. This says that the Fourier transform of the transition density of a Levy process has a particularly nice structureform, and has lead to many applications of spectral fourier theory to finance.

All non-Brownian Levy processes have heavier tails than Brownian motion. They are semimartingales, and thus one can define a sensible notion of stochastic integration with respect to a Levy process. As such, they make nice models for log asset proce processes, though they have many other applications in finance.

Take a look at Cont and Tankov's book - it's probably the friendliest introduction to Levy process I've seen. Other more theoretical books include those of Kyprianou, Applebaum and Sato (in approximate order of difficulty).

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A Levy process is a stochastic process with stationary, independent increments. These processes have a lot of structure - partly due to the Levy-Khintchine theorem. This says that the Fourier transform of the transition density of a Levy process has a particularly nice structure, and has lead to many applications of spectral theory to finance.

All non-Brownian Levy processes have heavier tails than Brownian motion. They are semimartingales, and thus one can define a sensible notion of stochastic integration with respect to a Levy process. As such, they make nice models for log asset proce processes, though they have many other applications in finance.

Take a look at Cont and Tankov's book - it's probably the friendliest introduction to Levy process I've seen. Other more theoretical books include those of Kyprianou, Applebaum and Sato (in approximate order of difficulty).

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