Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 201 / 6 / a

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- Solution a

Solution

A Lévy process

(X_{t})_{t \geq 0}

starts at zero, has independent and stationary increments, is stochastically continuous, and is taken with càdlàg sample paths. Thus for

0 \leq t_{0} < \dots < t_{n}

, the increments

X_{t_{j}} - X_{t_{j - 1}}

are independent, and the law of

X_{s + t} - X_{s}

depends only on

t

.

Solved by gpt-5.6-sol high.

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