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Martin Sleziak
Martin Sleziak
5:29 AM
2
Q: Malliavin derivative of Ito process

MrMMSLet $X_t= X_0 + \int_0^t \mu(s,X_s)ds + \int_0^t \sigma(s,X_s)dW_s$ where $\mu$ and $\sigma$ are $C^1$ functions satisfying the usual growth restriction and $W_t$ is a $d$-dimensional Brownian motion. Let $f\in C^2(\mathbb{R}^d;\mathbb{R})$ and let $D_t$ denote the Malliavin derivative at time $...

pr.probability stochastic-processes stochastic-calculus stochastic-differential-equations malliavin-calculus
Malliavin calculus
In probability theory and related fields, Malliavin calculus is a set of mathematical techniques and ideas that extend the mathematical field of calculus of variations from deterministic functions to stochastic processes. In particular, it allows the computation of derivatives of random variables. Malliavin calculus is also called the stochastic calculus of variations. Malliavin calculus is named after Paul Malliavin whose ideas led to a proof that Hörmander's condition implies the existence and smoothness of a density for the solution of a stochastic differential equation; Hörmander's original...
 

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