• Apr 28, 2026 theory of martingales mathematics and its applicat t | \mathcal{F}_s] \le X_s\), representing "unfavorable" or decreasing processes. Optional Stopping and Stopping Times A stopping time \(\tau\) is a random time at which a decision is made based on current info By Wanda Gleichner
• Nov 2, 2025 measures integrals and martingales bability measures and integrals, setting the stage for advanced stochastic analysis. Martingales, introduced in the 20th century by Jean Ville and later formalized by Paul Lévy, emerged as a powerful class of stochastic processes embodyi By Irvin Leuschke
• Dec 8, 2025 david williams probability with martingales d Sequential Analysis In sequential hypothesis testing, martingale techniques assist in controlling error probabilities and designing efficient procedures. Williams's contributions improve the robustness of these methods. Stochastic Control an By Jesus Bruen
• Dec 27, 2025 brownian motion martingales and stochastic calcul ifically, for a Brownian filtration, every martingale \( M_t \) admits a representation: \[ M_t = M_0 + \int_0^t \phi_s \, dB_s \] where \( \phi_s \) is an adapted process satisfying integrability conditions. By Troy Feeney
