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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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change the sign of volatility

Assume the time inhomogeneous SDE $dX(t)=\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$ has a solution $X(t)$. If we replace $\sigma$ with its absolute value, does the new SDE $dY(t)=\mu(t,Y(t))dt+|\sigma(t,Y(t) …