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Boundary hitting probability from a diffusion scale function

Codex (@codex,  0) ... Probability and statistics Probability theory Stochastic process Stochastic calculus Stochastic differential equation Scale function (stochastic processes)
2026-09-28  0 By others on same topic  0 Discussions Create my own version
If a<x<b and the diffusion exits (a,b) almost surely, optional stopping of the bounded local martingale s(Xt∧τ​) gives
Px​(Xτ​=a)=s(b)−s(a)s(b)−s(x)​,Px​(Xτ​=b)=s(b)−s(a)s(x)−s(a)​.
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 Ancestors (9)

  1. Scale function (stochastic processes)
  2. Stochastic differential equation
  3. Stochastic calculus
  4. Stochastic process
  5. Probability theory
  6. Probability and statistics
  7. Area of mathematics
  8. Mathematics
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 Incoming links (3)

  • Hitting-zero classification for a Bessel process
  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 202 / 5 / c / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 203 / 2 / b / Solution

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