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Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.

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Stochastic integral with respect to discontinuous martingale

in my research, I need to deal with a stochastic integral with respect to a compensated poisson process, namely, $ \int_0^t f(X_t) dM_t,$ where $M(t) = N(t) - \int_0^t \lambda(s)ds$. The integrand $ …
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