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Results tagged with pr.probability
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user 125179
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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A singular stochastic differential equation
We consider the following SDE:
$$dX_t = 1(X_t = 0) \, dt + 1(X_t >0) \, dB_t, \quad X_0= x > 0,$$
where $(B_t, \, t \ge 0)$ is linear Brownian motion.
Let $\tau: = \inf\{t >0: X_t = 0\}$ be the first …
