Dynkin's formula  In mathematics — specifically, in stochastic analysis — Dynkin's formula is a theorem giving the expected value of any suitably smooth statistic of an Itō diffusion at a stopping time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene Dynkin. Let "X" be the R"n"-valued Itō diffusion solving the stochastic differential equation  For a point "x" ∈ R"n", let P"x" denote the law of "X" given initial datum "X"0 = "x", and let E"x" denote expectation with respect to P"x". Let "A" be the infinitesimal generator of "X", defined by its action on compactly-supported "C"2 (twice differentiable with continuous second derivative) functions "f" : R"n" → R as  or, equivalently,  Let "τ" be a stopping time with E"x"["τ"] 2 with compact support. Then Dynkin's formula holds:  In fact, if "τ" is the first exit time for a bounded set "B" ⊂ R"n" with E"x"["τ"] 2 functions "f", without the assumption of compact support. Dynkin's formula can be used to find the expected first exit time "τ""K" of Brownian motion "B" from the closed ball  which, when "B" starts at a point "a" in the interior of "K", is given by  Choose an integer "j". The strategy is to apply Dynkin's formula with "X" = "B", "τ" = "σ""j" = min("j", "τ""K"), and a compactly-supported "C"2 "f" with "f"("x") = |"x"|2 on "K". The generator of Brownian motion is Δ/2, where Δ denotes the Laplacian operator. Therefore, by Dynkin's formula,  Hence, for any "j",  Now let "j" → +∞ to conclude that "τ""K" = lim"j"→+∞"σ""j"   Ted Petersen  Ted Petersen (born February 7, 1955) is a former professional American football player who played offensive lineman for nine seasons for the Pittsburgh Steelers, the Cleveland Browns, and the Indianapolis Colts.