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with 3 upcrossings of the interval [a,b]2023-02-28T02:10:16+00:00monthlyhttps://almostsuremath.com/2009/11/15/stopping-times-and-the-debut-theorem/2024-11-10T00:49:48+00:00monthlyhttps://almostsuremath.com/2009/10/25/integrating-with-respect-to-brownian-motion/2022-06-14T13:46:10+00:00monthlyhttps://almostsuremath.com/2009/12/06/martingales-and-elementary-integrals/2022-04-27T20:27:39+00:00monthlyhttps://almostsuremath.com/2010/05/25/the-martingale-representation-theorem/2022-03-21T23:40:20+00:00monthlyhttps://almostsuremath.com/2010/04/13/levys-characterization-of-brownian-motion/2023-09-16T00:20:23+00:00monthlyhttps://almostsuremath.com/2010/06/16/continuous-processes-with-independent-increments/2024-01-29T14:46:31+00:00monthlyhttps://almostsuremath.com/2022/03/06/martingale-marginals/2023-06-30T17:29:15+00:00monthlyhttps://almostsuremath.com/2022/02/25/the-collatz-conjecture/2023-01-07T06:05:15+00:00monthlyhttps://almostsuremath.com/2009/12/23/localization/2023-08-31T03:45:38+00:00monthlyhttps://almostsuremath.com/2010/01/18/quadratic-variations-and-integration-by-parts/2022-02-25T13:42:28+00:00monthlyhttps://almostsuremath.com/2020/10/07/the-stochastic-fubini-theorem/2022-02-25T13:24:15+00:00monthlyhttps://almostsuremath.com/2009/11/23/sigma-algebras-at-a-stopping-time/2025-12-01T17:14:09+00:00monthlyhttps://almostsuremath.com/2010/01/03/the-stochastic-integral/2024-03-19T07:08:05+00:00monthlyhttps://almostsuremath.com/2016/10/05/a-martingale-which-moves-along-a-deterministic-path/https://almostsuremath.com/wp-content/uploads/2016/10/martregions.pngmartregionshttps://almostsuremath.com/wp-content/uploads/2016/10/martpaths.pngmartpaths2021-04-07T11:54:30+00:00monthlyhttps://almostsuremath.com/2010/08/16/failure-of-the-martingale-property/2021-04-02T18:08:51+00:00monthlyhttps://almostsuremath.com/2010/07/28/bessel-processes/https://almostsuremath.com/wp-content/uploads/2010/07/besselprocess3.gifSquared 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s://almostsuremath.com/wp-content/uploads/2010/02/100125-sdes_fig1_crop.pngexistence-of-solutions-to-stochastic-differential-equations_fig1Approximate solution to the SDE 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continuous martingale with maximum 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solutions to r + 1 = 2^rComplex solutions to r+1=2^rhttps://almostsuremath.com/wp-content/uploads/2010/10/101001-asymptotics_fig3.gifFurther asymptotics of p(n)Further asymptotics of p(n)https://almostsuremath.com/wp-content/uploads/2010/10/101001-asymptotics_fig21.gifAsymptotics of p(n)Asymptotics of p(n)https://almostsuremath.com/wp-content/uploads/2010/10/101001-asymptotics_fig1.gifPlot of n*p(n) for odd and even pointsPlot of n*p(n) for odd and even points2020-09-15T14:12:24+00:00monthlyhttps://almostsuremath.com/2020/08/04/the-khintchine-inequality/2022-10-14T15:06:39+00:00monthlyhttps://almostsuremath.com/2010/03/25/preservation-of-the-local-martingale-property/2023-04-13T11:15:13+00:00monthlyhttps://almostsuremath.com/2010/03/22/martingales-are-integrators/2025-01-03T20:34:57+00:00monthlyhttps://almostsuremath.com/2010/04/06/the-burkholder-davis-gundy-inequality/2023-12-27T08:56:24+00:00monthlyhttps://almostsuremath.com/about/2024-04-21T16:20:14+00:00weekly0.6https://almostsuremath.com/2010/07/19/properties-of-feller-processes/2023-10-15T04:44:37+00:00monthlyhttps://almostsuremath.com/2010/06/24/poisson-processes/https://almostsuremath.com/wp-content/uploads/2010/06/compensatedpoisson1.pngCompensatedPoissonA compensated Poisson processhttps://almostsuremath.com/wp-content/uploads/2010/06/poissonprocess2.pngPoissonProcessA Poisson process sample path2020-07-31T08:45:20+00:00monthlyhttps://almostsuremath.com/2016/08/14/purely-discontinuous-semimartingales/2020-06-23T13:25:55+00:00monthlyhttps://almostsuremath.com/2010/07/14/feller-processes/2020-06-15T16:34:00+00:00monthlyhttps://almostsuremath.com/2018/12/23/projection-in-discrete-time/2019-12-14T01:16:35+00:00monthlyhttps://almostsuremath.com/2019/01/07/proof-of-optional-and-predictable-section/2019-12-16T17:03:32+00:00monthlyhttps://almostsuremath.com/2019/02/24/properties-of-the-dual-projections/2019-10-29T17:59:41+00:00monthlyhttps://almostsuremath.com/2019/02/08/dual-projections/2021-04-27T10:05:19+00:00monthlyhttps://almostsuremath.com/2019/01/20/properties-of-optional-and-predictable-projections/2021-02-15T21:38:27+00:00monthlyhttps://almostsuremath.com/2017/03/06/the-projection-theorems-2/2019-10-29T17:44:32+00:00monthlyhttps://almostsuremath.com/2017/02/28/pathwise-regularity-of-optional-and-predictable-processes/2024-03-02T20:29:00+00:00monthlyhttps://almostsuremath.com/2016/11/22/predictable-processes/2023-06-27T00:58:54+00:00monthlyhttps://almostsuremath.com/2016/11/15/optional-processes/2019-10-29T17:18:29+00:00monthlyhttps://almostsuremath.com/2016/07/02/properties-of-quasimartingales/2019-10-28T18:54:34+00:00monthlyhttps://almostsuremath.com/2011/12/30/the-doob-meyer-decomposition/2019-10-28T18:52:11+00:00monthlyhttps://almostsuremath.com/2011/07/18/predictable-fv-processes/2022-02-20T17:11:15+00:00monthlyhttps://almostsuremath.com/2010/09/15/processes-with-independent-increments/2024-09-02T07:32:37+00:00monthlyhttps://almostsuremath.com/2010/07/12/markov-processes/2024-07-28T21:27:07+00:00monthlyhttps://almostsuremath.com/2010/05/17/sdes-under-changes-of-time-and-measure/2022-12-31T22:03:24+00:00monthlyhttps://almostsuremath.com/2010/04/20/time-changed-brownian-motion/2024-01-18T00:23:42+00:00monthlyhttps://almostsuremath.com/2019/01/21/pathwise-properties-of-optional-and-predictable-projections/2019-01-19T23:15:06+00:00monthlyhttps://almostsuremath.com/2016/11/29/the-section-theorems/2016-11-30T17:01:46+00:00monthlyhttps://almostsuremath.com/2016/11/08/measurable-projection-and-the-debut-theorem/2016-11-10T23:55:28+00:00monthlyhttps://almostsuremath.com/2016/11/01/predictable-projection-for-left-continuous-processes/2016-11-08T02:02:37+00:00monthlyhttps://almostsuremath.com/2016/10/25/optional-projection-for-right-continuous-processes/2016-10-31T22:36:30+00:00monthlyhttps://almostsuremath.com/2011/12/27/compensators-of-counting-processes/2016-10-30T04:01:33+00:00monthlyhttps://almostsuremath.com/2016/07/25/constructing-martingales-with-prescribed-jumps/2021-04-17T03:19:37+00:00monthlyhttps://almostsuremath.com/2011/10/03/special-semimartingales/2016-10-23T00:59:38+00:00monthlyhttps://almostsuremath.com/2012/04/12/quasimartingales/2016-10-22T13:52:55+00:00monthlyhttps://almostsuremath.com/2016/10/21/the-projection-theorems/2017-05-20T12:29:40+00:00monthlyhttps://almostsuremath.com/2010/11/23/levy-processes/https://almostsuremath.com/wp-content/uploads/2010/10/cauchyprocess2.pngCauchy ProcessA Cauchy process sample path2017-02-10T09:05:24+00:00monthlyhttps://almostsuremath.com/2016/08/08/purely-discontinuous-local-martingales/2016-08-09T19:04:56+00:00monthlyhttps://almostsuremath.com/2011/12/20/compensators-of-stopping-times/2023-09-15T13:54:27+00:00monthlyhttps://almostsuremath.com/2016/07/18/the-doob-meyer-decomposition-for-quasimartingales/2016-07-18T00:21:06+00:00monthlyhttps://almostsuremath.com/2011/03/28/the-bichteler-dellacherie-theorem/2016-07-17T22:51:49+00:00monthlyhttps://almostsuremath.com/2012/06/18/raos-quasimartingale-decomposition/2017-12-01T16:18:02+00:00monthlyhttps://almostsuremath.com/2009/09/27/the-gaussian-correlation-conjecture/2016-06-06T23:43:47+00:00monthlyhttps://almostsuremath.com/2011/11/22/compensators/2021-03-21T18:15:07+00:00monthlyhttps://almostsuremath.com/2010/05/03/girsanov-transformations/2024-11-02T10:40:21+00:00monthlyhttps://almostsuremath.com/using-latex-in-comments/2014-01-17T23:25:13+00:00weekly0.6https://almostsuremath.com/2011/03/11/the-general-theory-of-semimartingales/2018-07-02T14:03:01+00:00monthlyhttps://almostsuremath.com/2009/10/31/stochastic-calculus-notes/2022-01-04T01:38:16+00:00monthlyhttps://almostsuremath.com/2010/04/12/special-processes/2011-10-27T14:59:18+00:00monthlyhttps://almostsuremath.comdaily1.02025-12-01T17:48:45+00:00